Binary carry or borrow look-ahead circuit

The present invention relates to a binary operator, more particularly, to a carry select adder circuit (CSA: including a borrow select subtracter in a parallel full subtracter) and a block look ahead carry generator circuit (BLACG: including a block look ahead borrow generator circuit in a parallel full subtracter) in a parallel full adder.

Recently, along with the increase in the amounts of data, a demand has arisen for higher speeds of data processing by operators. As one means for achieving high speed data processing, a carry look ahead (CLA) method may be used. This carry look ahead method attempts to achieve high speed in the speed of addition by looking ahead at the necessary carry operation for each digit in advance. However, according to this carry look ahead method, an increase in the data length is accompanied with an inconveniently large increase in the operation elements and so is not practical.

On the other hand, when the data length is particularly long (for example, 32 bits, 64 bits), a carry select adder (CSA) method may be a suitable method. According to the carry select adder method, before the data is divided into a plurality of blocks and the real carry signal from the lower block is generated in the adders of the various blocks, a sum signal in the case of assumption of the carry being "0" and a sum signal in the case of assumption of the carry being "1" are respectively generated. At the point of time when the real carry signal coming up from the adder of the lower block is input, selection is made of the presumed sum signal (one of "0" or "1") corresponding to the logic of the real carry signal and that selected presumed sum signal is output as the real sum signal of the block adder.

In the prior art, a binary adder circuit using the block select look ahead system for cutting down on the number of elements of the circuit is shown in Japanese Unexamined Patent Publication (Kokai; JP, A) No. 60-105041. However, the adder circuit of JPA '041 is used for generating a real carry signal, and not generating a real sum signal. Further, the adder circuit does not generate directly by using a cumulative carry propagate signal and a cumulative carry generate signal, since the adder circuit does not comprise a cumulative carry propagate signal generating unit and a cumulative carry generate signal generating unit.

Reference is further made to Computer Arithmetic. Principles, Architecture and design. Kai Hwang. US-New York.

It is desirable to provide a binary operator using a carry select adder or subtracter method, in which binary operator it is possible to cut down on the number of component elements of the circuit without sacrificing high speed.

According to a first embodiment of the present invention there is provided a binary operator, having a carry propagate signal and a carry generate signal generating unit which receives two pieces of n-bit binary data and generates a carry propagate signal and a carry generate signal of various digits. The two pieces of n-bit binary data are divided into blocks of a predetermined number of bits, each data of the divided blocks is processed in parallel by a plurality of block adders based on the corresponding carry propagate signal and carry generate signal, and a real sum signal is output by calculating the arithmetic sum of the two n-bit binary data. The binary operator comprises a cumulative carry propagate signal generating unit, a cumulative carry generate signal generating unit and a real sum signal generating unit.

The cumulative carry propagate signal generating unit is connected to the carry propagate signal and carry generate signal generating unit and receives carry propagate signals of the various digits in the block adders to generate a cumulative carry propagate signal by calculating the carry propagate signals. The cumulative carry generate signal generating unit is connected to the carry propagate signal and carry generate signal generating unit and receives the carry propagate signals and carry generate signals of the various digits in the block adders to generate a cumulative carry generate signal by calculating the carry propagate signals and the carry generate signals.

The real sum signal generating unit is connected to the carry propagate signal and carry generate signal generating unit, the cumulative carry propagate signal generating unit and the cumulative carry generate signal generating unit, and receives the carry propagate signal of various digits, the cumulative carry propagate signal from the cumulative carry propagate signal generating unit, the cumulative carry generate signal from the cumulative carry generate signal generating unit and a real carry signal to generate the real sum signal by calculating the carry propagate signal, the cumulative carry propagate signal, the cumulative carry generate signal and the real carry signal.

An i-th digit of the real sum signal generating unit may generate the real sum signal of said i-th digit by calculating the carry propagate signal of the i-th digit, the cumulative carry propagate signal of the (i-l)-th digit, the cumulative carry generate signal of the (i-l)-th digit and a real carry signal advanced from the lower digit to the block adder to which it belongs.

The binary operator may comprise a plurality of carry select adder circuits, and each carry select adder circuit may include the cumulative carry propagate signal generating unit, the cumulative carry generate signal generating unit and the real sum signal generating unit made of combinations of logic gate circuits using, for instance, CMOS transistors.

The cumulative carry propagate signal generating unit and the cumulative carry generate signal generating unit may comprise a chain circuit mutually connected with a transfer gate circuit and an inverter circuit, if they are implemented in CMOS circuits.

According to a second embodiment of the present invention, there is also provided a binary operator, having a borrow propagate signal and borrow generate signal generating unit which receives two pieces of n-bit binary data and generates a borrow propagate signal and a borrow generate signal of various digits. The two pieces of n-bit binary data are divided into blocks of predetermined number of bits, each data of the divided blocks is processed in parallel by a plurality of block subtracters based on the corresponding borrow propagate signal and borrow generate signal, and a real difference signal is output by calculating the arithmetic difference of the two n-bit binary data. The binary operator comprises a cumulative borrow propagate signal generating unit, a cumulative borrow generate signal generating unit and a real difference signal generating unit.

The cumulative borrow propagate signal generating unit is connected to the borrow propagate signal and borrow generate signal generating unit and receives borrow propagate signals of the various digits in the block subtracters to generate a cumulative borrow propagate signal by calculating the borrow propagate signals. The cumulative borrow generate signal generating unit is connected to the borrow propagate signal and borrow generate signal generating unit and receives the borrow propagate signals and borrow generate signals of the various digits in the block subtracters to generate a cumulative borrow generate signal by calculating the borrow propagate signals and the borrow generate signals.

The real difference signal generating unit is connected to the borrow propagate signal and borrow generate signal generating unit, the cumulative borrow propagate signal generating unit and the cumulative borrow generate signal generating unit, and receives the borrow propagate signal of various digits, the cumulative borrow propagate signal from the cumulative borrow propagate signal generating unit, the cumulative borrow generate signal from the cumulative borrow generate signal generating unit and a real borrow signal to generate the real difference signal by calculating the borrow propagate signal, the cumulative borrow propagate signal, the cumulative borrow generate signal and the real borrow signal.

An i-th digit of the real difference signal generating unit may generate the real difference signal of the i-th digit by calculating the borrow propagate signal of the i-th digit, the cumulative borrow propagate signal of the i-th digit, the cumulative borrow generate signal of the (i-1)-th digit and a real borrow signal advanced from the lower digit to the block subtracter to which it belongs.

The binary operator may comprise a plurality of borrow select subtracter circuits, each of the borrow select subtracter circuits may include the cumulative borrow propagate signal generating unit, the cumulative borrow generate signal generating unit and the real difference signal generating unit made of combinations of logic gate circuits using, for instance, CMOS transistors.

The cumulative borrow propagate signal generating unit and the cumulative borrow generate signal generating unit may comprise a chain circuit mutually connected with a transfer gate circuit and an inverter circuit, if they are implemented in CMOS circuits.

According to a third embodiment of the present invention, there is provided a binary operator which comprises a carry propagate signal and carry generate signal generating unit, a block addition unit, connected to the carry propagate signal and carry generate signal generating unit, a block carry propagate signal and block carry generate signal generating unit, a cumulative block carry propagate signal and cumulative block carry generate signal generating unit and a real carry signal generating unit. The carry propagate signal and carry generate signal generating unit receives two pieces of n-bit binary data to generate a carry propagate signal and a carry generate signal of various digits.

The block addition unit is connected to the carry propagate signal and carry generate signal generating unit and receives a real carry signal and the carry propagate signal and the carry generate signal from the carry propagate signal and carry generate signal generating unit to divide the two pieces of n-bit binary data into blocks of predetermined number of bits, and to process in parallel based on the carry propagate signal and the carry generate signal corresponding to each data of the divided blocks and generate a real sum signal by calculating the arithmetic sum of the two n-bit binary data. The block carry propagate signal and block carry generate signal generating unit is connected to the carry propagate signal and carry generate signal generating unit and receives the carry propagate signal and the carry generate signal from the carry propagate signal and carry generate signal generating unit to generate a block carry propagate signal and a block carry generate signal by the carry propagate signal and the carry generate signal corresponding to each data of the divided blocks.

The cumulative block carry propagate signal and cumulative block carry generate signal generating unit is connected to the block carry propagate signal and block carry generate signal generating unit and receives the block carry propagate signal and the block carry generate signal from the block carry propagate signal and block carry generate signal generating unit to generate a cumulative block carry propagate signal and a cumulative block carry generate signal using the block carry propagate signal and the block carry generate signal. The real carry signal generating unit is connected to the cumulative block carry propagate signal and cumulative block carry generate signal generating unit and the block addition unit and receives a carry signal, the cumulative block carry propagate signal and the cumulative block carry generate signal from the cumulative block carry propagate signal and cumulative block carry generate signal generating unit to generate a real carry signal by the carry signal, the cumulative block carry propagate signal and the cumulative block carry generate signal.

The block addition unit may generate presumed sum signals in the cases of the carry signal output from the real carry signal generating unit being "0" and "1", and selects one of said presumed sum signals in accordance with the content of the real carry signal from the real carry signal generating means.

The binary operator may comprise a plurality of block look ahead carry generator circuits, and each block look ahead carry generator circuit may include the cumulative block carry propagate signal and cumulative block carry generate signal generating unit and the real carry signal generating unit made of combinations of logic gate circuits and transfer gate circuits using CMOS transistors.

The binary operator may comprise a plurality of block look ahead carry generator circuits made of a chain circuit mutually connected with a transfer gate circuit and an inverter circuit. The binary operator may comprise a plurality of block look ahead carry generator circuit constructed by one or more stages.

According to a fourth embodiment of the present invention, there is also provided a binary operator which comprises a borrow propagate signal and borrow generate signal generating unit, a block subtraction unit, connected to the borrow propagate signal and borrow generate signal generating unit, a block borrow propagate signal and block borrow generate signal generating unit, a cumulative block borrow propagate signal and cumulative block borrow generate signal generating unit and a real borrow signal generating unit. The borrow propagate signal and borrow generate signal generating unit receives two pieces of n-bit binary data to generate a borrow propagate signal and a borrow generate signal of various digits.

The block subtraction unit is connected to the borrow propagate signal and borrow generate signal generating unit and receives a real borrow signal and the borrow propagate signal and the borrow generate signal from the borrow propagate signal and borrow generate signal generating unit to divide the two pieces of n-bit binary data into blocks of a predetermined number of bits, and to process in parallel based on the borrow propagate signal and the borrow generate signal corresponding to each data of the divided blocks and generate a real difference signal by calculating the arithmetic difference of the two n-bit binary data. The block borrow propagate signal and block borrow generate signal generating unit is connected to the borrow propagate signal and borrow generate signal generating unit and receives the borrow propagate signal and the borrow generate signal from the borrow propagate signal and borrow generate signal generating unit to generate a block borrow propagate signal and a block borrow generate signal by the borrow propagate signal and the borrow generate signal corresponding to each data of the divided blocks.

The cumulative block borrow propagate signal and cumulative block borrow generate signal generating unit is connected to the block borrow propagate signal and block borrow generate signal generating unit and receives the block borrow propagate signal and the block borrow generate signal from the block borrow propagate signal and block borrow generate signal generating unit to generate a cumulative block borrow propagate signal and a cumulative block borrow generate signal using the block borrow propagate signal and the block borrow generate signal. The real borrow signal generating unit is connected to the cumulative block borrow propagate signal and cumulative block borrow generate signal generating unit and the block subtraction unit and receives a borrow signal, the cumulative block borrow propagate signal and the cumulative block borrow generate signal from the cumulative block borrow propagate signal and cumulative block borrow generate signal generating unit to generate a real borrow signal by the borrow signal, the cumulative block borrow propagate signal and the cumulative block borrow generate signal.

The block subtraction unit may generate presumed difference signals in the cases of the borrow signal output from the real borrow signal generating unit being "0" and "1", and selects one of said presumed difference signals in accordance with the content of the real borrow signal from the real borrow signal generating means.

The binary operator may comprise a plurality of block look ahead borrow generator circuits, each of the block look ahead borrow generator circuit may include the cumulative block borrow propagate signal and cumulative block borrow generate signal generating unit and the real borrow signal generating unit made of combinations of logic gate circuits and transfer gate circuit using CMOS transistors.

The binary operator may comprise a plurality of block look ahead borrow generator circuits made of a chain circuit mutually connected with a transfer gate circuit and an inverter circuit. The binary operator may comprise a plurality of block look ahead borrow generator circuit constructed by one or more stages.

Reference will now be made, by way of example, to the accompanying drawings, wherein: <ul id="ul0001" list-style="none" compact="compact"><li>Figure 1 is a block diagram showing an example of application of a parallel full adder to a 64 bit ALU;</li><li>Fig. 2 is a circuit diagram showing an example of a CSA circuit in the parallel full adder shown in Fig. 1;</li><li>Fig. 3 is a circuit diagram showing an example of a BLACG circuit in the parallel full adder shown in Fig. 1;</li><li>Fig. 4 is a block diagram showing a first embodiment of a binary operator according to the present invention;</li><li>Fig. 5 is a block diagram showing a second embodiment of a binary operator according to the present invention;</li><li>Fig. 6 is a block diagram showing an example of application to a 64 bit ALU of a parallel full adder according to the first embodiment of the present invention;</li><li>Fig. 7(a) is a block diagram showing a CSA circuit in the parallel full adder shown in Fig. 6, and Fig. 7(b) is a circuit diagram showing a first example of the CSA circuit shown in Fig. 7(a);</li><li>Fig. 8 is a circuit diagram showing a first modification of the real sum signal generating circuit shown in Fig. 7(b);</li><li>Fig. 9 is a circuit diagram showing a second modification of the real sum signal generating circuit shown in Fig. 7(b);</li><li>Fig. 10 is a circuit diagram showing a third modification of the real sum signal generating circuit shown in Fig. 7(b);</li><li>Fig. 11 is a circuit diagram showing a fourth modification of the real sum signal generating circuit shown in Fig. 7(b);</li><li>Fig. 12 is a circuit diagram showing a fifth modification of the real sum signal generating circuit shown in Fig. 7(b);</li><li>Fig. 13(a) is a block diagram showing a CSA circuit in the parallel full adder shown in Fig. 6, and Fig. 13(b) is a circuit diagram showing a second example of the CSA circuit shown in Fig. 13(a);</li><li>Fig. 14 is a block diagram showing a third embodiment of a binary operator according to the present invention;</li><li>Fig. 15 is a block diagram showing a fourth embodiment of a binary operator according to the present invention;</li><li>Fig. 16 is a block diagram showing a first example of application to a 64 bit ALU of a parallel full adder according to the third embodiment of the present invention;</li><li>Fig. 17(a) is a block diagram showing a BLACG circuit in the parallel full adder shown in Fig. 16, and Fig. 17(b) is a circuit diagram showing a first example of the BLACG circuit shown in Fig. 17(a);</li><li>Fig. 18 is a circuit diagram showing a first modification of the BLACG circuit shown in Fig. 17(b);</li><li>Fig. 19 is a circuit diagram showing a second modification of the BLACG circuit shown in Fig. 17(b);</li><li>Fig. 20 is a circuit diagram showing a third modification of the BLACG circuit shown in Fig. 17(b);</li><li>Fig. 21 is a circuit diagram showing a fourth modification of the BLACG circuit shown in Fig. 17(b);</li><li>Fig. 22 is a circuit diagram showing a fifth modification of the BLACG circuit shown in Fig. 17(b);</li><li>Fig. 23 is a circuit diagram showing a sixth modification of the BLACG circuit shown in Fig. 17(b);</li><li>Fig. 24(a) is a block diagram showing a BLACG circuit in the parallel full adder shown in Fig. 16, and Fig. 24(b) is a circuit diagram showing a second example of the BLACG circuit shown in Fig. 24(a);</li><li>Fig. 25 is a block diagram showing a second example of application to a 64 bit ALU of a parallel full adder according to the third embodiment of the present invention;</li><li>Fig. 26(a) is a block diagram showing a BLACG circuit in the parallel full adder shown in Fig. 25, and Fig. 26(b) is a circuit diagram showing a third example of the BLACG circuit shown in Fig. 26(a); and</li><li>Fig. 27(a) is a block diagram showing a BLACG circuit in the parallel full adder shown in Fig. 25, and Fig. 27(b) is a circuit diagram showing a fourth example of the BLACG circuit shown in Fig. 27(a).</li></ul>

Figure 1 shows an example of an arithmetic logic unit (ALU) of 64 bits including a high speed parallel full adder using carry select adder method as known from the Hwang citation.

This ALU is comprised, roughly, of a sum signal generating circuit which generates various presumed sum signals in the case of the real carry signal being "0" and in the case of it being "1" by the look ahead method, a carry signal generating circuit which generates various presumed carry signals in the case of the real carry signal being "0" and in the case of it being "1" by the same look ahead method, and a selection circuit which selects the above-mentioned sum signal according to the logic of the real carry signal which is generated. Below, this will be explained with reference to Fig. 1 by the various constituent elements.

Processing Data

The data to be processed are in general the two pieces of n-bit binary data A and B. Here, they are considered to be 64 bit data. A is the augend and B the addend. ALU calculates the arithmetic sum F of the augend A and the addend B.

In the following explanation, matters are generalized so as to simplify the explanation. The bits of the i-th digits of the data A and B and the arithmetic sum F (i = 0, 1, 2, ... n-1) are designated as A_i , B_i , and F_i. The character "i" is appended to other signals in expressing the same.

The above-mentioned 64 bit input data A (A₀ , A₁ , A₂ , ... A₆₃) and B (B₀ , B₁ , B₂ , ... B₆₃) is input to the unit logic block circuits (below, ULB) 100.

ULB Circuit 100

A ULB circuit 100 is provided corresponding to each bit of the digits of the input and output data and thus 64 are provided, i.e., 0 to 63. The ULB circuit 100 generates the necessary signals (that is, the two signals of the carry propagate signal P_i and the carry generate signal G_i) for the carry select addition at later stages.

Here, the carry propagate signal P_i is given by the logical EOR:<maths id="math0001" num="(1)"><math display="block"><mrow><msub><mrow><mtext>P</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext> = A</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext> ⊕ B</mtext></mrow><mrow><mtext>i</mtext></mrow></msub></mrow></math><img file="EP0347029B1_D0001.tif" /></maths> Further, the carry generate signal G is given by the logical AND:<maths id="math0002" num="(2)"><math display="block"><mrow><msub><mrow><mtext>G</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext> = A</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext>·B</mtext></mrow><mrow><mtext>i</mtext></mrow></msub></mrow></math><img file="EP0347029B1_D0002.tif" /></maths>

The carry propagate signal P_i and the carry generate signal G_i generated in this way are input into the block carry select adder circuit (CSA) 101 of the blocks to which they respectively belong.

Note that the signals I₀ to I₃ given to the ULB circuits 100 are signals for designating what should be output as the carry propagate signal P_i and the carry generate signal G_i and are not directly related to the composition of the adder of the present invention and thus an explanation of the same is omitted.

CSA Circuit 101

An array of CSA circuits 101 divide the input data A and B into blocks of predetermined numbers of bits (in this example, 4 bits). In each block, the CSA circuit generates presumed sum signals F_i(0) and F_i(1) for each of the bits belonging to the blocks before the real carry signal C_M-1 from the lower block is generated. Note that M shows the lowest digit of the signal to be processed in the block adder (CSA circuit) to which the i-th digit belongs. Further, the number of signal digits processed in a block adder is m′. The presumed sum signal F_i(0) shows the presumed sum signal in the case where the real carry signal C_M-1 is presumed to be "0" and F_i(1) that in the case where the real carry signal C_M-1 is presumed to be "1". Further, the CSA circuit 101, in addition to the above-mentioned sum signals F_i(0) and F_i(1) , generates the block carry propagate signal BP_M+m-1 and the block carry generate signal BG_M+m-1 for use by the block look ahead carry generator circuit (BLACG), mentioned later.

Figure 2 shows a specific example of the CSA circuit 101, explained below. This Fig. 2 shows the example of a CSA circuit 101_-1 of the first block (block receiving input data A₀ to A₃ and B₀ to B₃) in Fig. 1. In Fig.2, (a) is a symbolized view and (b) is a detailed circuit diagram.

As shown in Fig. 2(b), the CSA circuit 101_-1 receives as input the carry propagate signals P₀ to P₃ and the carry generate signals G₀ to G₃ corresponding to the bits from four of the ULB circuits 100. As the constituent elements of the CSA circuit 101, the circuit is comprised of a combination of a NAND circuit, inverter circuit, and EOR circuit using CMOS transistors. Note that it is of course possible to comprise the same using bipolar transistors, NMOS transistors, HEMTs, MESFETs or other kinds of transistors.

The CSA circuit 101_-1 is roughly comprised of five parts. In the first part, presumed sum signals F₀(0) and F₀(1) relating to the 0th bit are generated. In the second part, the presumed sum signals F₁(0) and F₁(1) relating to the first bit are generated. In the third part, the presumed sum signals F₂(0) and F₂(1) relating to the second bit are generated. In the fourth part, the presumed sum signals F₃(0) and F₃(1) relating to the third bit are generated. Further, in the fifth part, the block carry propagate signal BP₃ and the block carry generate signal BG₃ relating to the third bit (that is, the highest digit in the first part) are generated. (partial circuit 103).

The various presumed sum signals F₀(0) , F₀(1) to F₃(0) , and F₃(1) generated in this way are output in the select waiting state to the corresponding first multiplexer circuit (below, called first MPX circuit) 102. Further, the block carry propagate signal BP₃ and the block carry generate signal BG₃ are output as part of the input signals of the BLACG circuit 105.

Above, the explanation was made with reference to a single CSA circuit 101_-1, but the same construction applies for corresponding input data in the case of CSA circuits of other blocks, so explanations of the same will be omitted.

BLACG Circuit 105

Each of a plurality of BLACG circuits 105 receives the block carry propagate signal BP_M+m-1 and the block carry generate signal BG_M+m-1 from the partial circuit 103 (Fig. 2(b)) in the CSA circuits 101 of a predetermined number of blocks (in this case, four) and generates the presumed carry signals C_i(0) and C_i(1) for each of the block carry propagate signal BP_i and the block carry generate signal BG_i connected to it, before the real carry signal C_M'-m' from the lower block is generated. M' shows the lowest digit of the signal to be processed in the BLACG circuit to which the circuit generating the i-th digit presumed carry signals C_i(0) and C_i(1) belongs. Further, m' is a positive integer which is usually equal to m. The presumed carry signal C_i(0) is the signal in the case where the real carry signal C_M'-m' is "0" and C_i(1) is that in the case where C_M'-m' is "1".

Figure 3 shows a specific example of the BLACG circuit 105, which is explained below. Figure 3 takes as an example the BLACG circuit 105_-1 of the first block (block dealing with the input signals BP₃, BG₃, BP₇ , BG₇ , BP₁₁ , BG₁₁ , BP₁₅ , and BG₁₅) in Fig. 1. In Fig. 3, (a) is a symbolized view of the BLACG circuit 105_-1 and (b) a detailed circuit diagram.

As shown in Fig. 3(b), the BLACG circuit 105_-1 receives as input the block carry propagate signals BP₃, BP₇ , BP₁₁ , and BP₁₅ and the block carry generate signals BG₃, BG₇ , BG₁₁ , and BG₁₅ from the partial circuit 103 of the CSA circuits 101 at the former stage. The BLACG circuit is comprised of a combination of a NAND circuit and inverter circuit using CMOS transistors. Note that it is not limited to CMOS transistors and that use may also be made of bipolar or other kinds of transistors for the construction.

The BLACG circuit 105_-1 is roughly comprised of four part. In the first part, presumed carry signals C₃(0) and C₃(1) are generated based on the block carry propagate signal BP₃ and the block carry generate signal BG₃. Below, in the same way, in the second part, C₇(0) and C₇(1) are generated based on BP₃ , BG₃ , BP₇ , and BG₇. In the third part, C₁₁(0) and C₁₁(1) are generated based on BP₃ , BG₃ , BP₇, BP₁₁ and BG₁₁. In the fourth part, C₁₅(0) and C₁₅(1) are generated based on BP₃ , BG₃ , BP₇ , BG₇, BP₁₁, BG₁₁, BP₁₅ and BG₁₅.

The various presumed carry signals C₃(0), C₃(1), C₇(0), C₇(1), C₁₁(0), C₁₁(1), C₁₅(0), and C₁₅(1) generated in this way are output in the select waiting state to the corresponding multiplexer circuit (below, called second MPX circuit) 104.

Above, the explanation was made with reference to a single BLACG circuit 105_-1 , but the same construction applies for BLACG circuits of other blocks, so explanations of the same will be omitted.

Second MPX Circuit 104

Each second MPX circuit 104 is a selector which selects one of the presumed carry signal pairs C₃(0), C₃(1) ... ( that is, one of carry "0" or "1") out of the presumed carry signal pair C₃(0), C₃(1) to C₁₅(0) , C₁₅(1) from the corresponding BLACG circuit 105 at the time of the input of the real carry signals C_in , C₁₅ , C₃₁ , and C₄₇ , which are the signals of the highest digits of the second MPX circuit 104 of the lower block.

The selection operation of the presumed carry signal starts by the input of the real carry signal C_in to the second MPX circuit 104 of the lowest block. At the time of the completion of the selection of the first block, the highest carry signal C₁₅ is moved up as the real carry signal for the next higher second MPX circuit 104 and after that is moved up successively toward the higher blocks.

On the other hand, the real carry signals C₃ to C₁₅ , C₁₉ to C₃₁ , C₃₅ to C₄₇ , and C₅₁ to C₆₃ , which are presumed carry signals selected in the second MPX circuits 104, are output as select signals to the corresponding first MPX circuits 102.

<u>First MPX Circuit 102</u> Each first MPX circuit 102 receives a carry signal C_M-1 (i.e. one of the carry signals C₃ to C₁₅ , C₁₉ to C₃₁ , C₃₅ to C₄₇ , and C₅₁ to C₆₃) from the corresponding second MPX circuit 104 and selects and outputs one of the presumed sum signals F_i(0) and F_i(1) output from the CSA circuits 101. The selection is performed in accordance with the contents of the carry signal C_M-1 input to the first MPX circuit 102. The selected presumed sum signal F_i(0) or F_i(1) is output as the real sum signal (specifically, F₀ to F₆₃) in the CSA circuit 101, whereby one block of an addition operation is ended.

Note that the signal (L, P_i) given to the first MPX circuit 102 is a signal for designating what should be output as F_i and is not directly related to the composition of the adder embodying the present invention and thus an explanation of the same is omitted along with the related MPX circuit.

The above explanation was made in reference to the example of a parallel full adder, but may be applied to a parallel full subtracter as well. In constructing a parallel full subtracter, for the i-th digit, a borrow propagate signal generated by the ULB circuit 100 is used as P_i and the borrow generate signal is used as G_i. That is, in subtraction where A is the minuend and B is the subtrahend, the borrow propagate signal P_i is found by the ENOR (i.e., exclusive - NOR operation) of:<maths id="math0003" num="(3)"><math display="block"><mrow><msub><mrow><mtext>P</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext> = </mtext><mover accent="true"><mrow><msub><mrow><mtext>A</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext> ⊕ B</mtext></mrow><mrow><mtext>i</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0003.tif" /></maths> Further, the borrow generate signal G_i may be found by<maths id="math0004" num="(4)"><math display="block"><mrow><msub><mrow><mtext>G</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext> = </mtext><mover accent="true"><mrow><msub><mrow><mtext>A</mtext></mrow><mrow><mtext>i</mtext></mrow></msub></mrow><mo>¯</mo></mover><msub><mrow><mtext>·B</mtext></mrow><mrow><mtext>i</mtext></mrow></msub></mrow></math><img file="EP0347029B1_D0004.tif" /></maths> In addition to this, by treating the carry signal as the borrow signal and processing the borrow signals successively from the lower digits, it is possible to construct a full subtracter by the same method of construction as above. However, the real difference signals F_i of the digits are found by the logical ENOR of:<maths id="math0005" num=""><math display="block"><mrow><msub><mrow><mtext>F</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext> = </mtext><mover accent="true"><mrow><msub><mrow><mtext>P</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext> ⊕ C</mtext></mrow><mrow><mtext>i-1</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0005.tif" /></maths>

As explained above, the parallel full adder using the carry select adder method is superior in functional aspects and shows its power in the case of high speed processing of 32-bit, 64-bit, and other long data.

However, in the above-mentioned parallel full adder using the carry select adder method, there may be problems of a larger number of constituent elements of the circuits - double the number of constituent elements compared with the simple ripple carry method.

That is, this is because the above-mentioned example prepares two presumed sum signals F_i(0) and F_i(1) in advance and outputs one of the presumed sum signals F_i(0) or F_i(1) as the real sum signal F_i at the time when the content of the carry signal from the lower digit to the said block adder (CSA circuit) is determined, so it is necessary that the two presumed sum signals F_i(0) and F_i(1) be generated in parallel (at the same time).

The circuit required for generating in parallel the two presumed sum signals F_i(0) and F_i(1) in the block adder (CSA circuit) processes, for the i-th digit, the carry propagate signal P_i and the carry generate signal G_i of the digits in the block adder to which the said i-th digit belongs and includes a considerable amount of overlapping portions (that is, portions which generate the same type of signals overlappingly). If these overlapping portions can be eliminated to an extent not obstructing the high speed of the carry select adder method, it would be possible to simplify the circuit construction and to reduce the number of constituent elements of the circuit. Of course, the two signals of the presumed sum signals F_i(0) and F_i(1) contain redundant information in generating the real sum signals F_i of the digits.

Further, in the above-mentioned parallel full adder using the carry select adder method, there are the problems of a larger number of constituent elements of the BLACG circuit 105 - double the number of constituent elements compared with the simple CLA method.

That is, this is because the above-mentioned example prepares two presumed sum signals F_i(0) and F_i(1) in the CSA circuit 101 in advance and selects and outputs one of the presumed sum signals F_i(0) or F_i(1) as the real sum signal F_i at the time when the content of the real carry signal generated by the BLACG circuit 105 is determined in accordance with the content thereof. Therefore, the operation speed is determined by how quickly the real carry signal can be generated. Here, to generate the real carry signal at a high speed, as mentioned above, the BLACG circuits 105 divide the data into blocks of four digits each, prepare two presumed carry signals C_i(0) and C_i(1) by the look ahead processing method, and select and output as the real carry signal C. one of the presumed carry signals C_i(0) or C_i(1) at the point of time when the real carry signal C_M'-m' from the lower digit is confirmed in the second MPX circuit 104. As a result of this construction, it is necessary to generate in parallel two resumed carry signals C_i(0) and C_i(1). The generating circuit for this parallel generation is a cause behind the increase in the number of circuit elements.

The circuit required for generating in parallel the two presumed carry signals C_i(0) and C_i(1) in the BLACG circuit 105 processes, for the i-th digit, the block carry propagate signal BP_i and the block carry generate signal BG_i of the digits in the BLACG circuit 105 to which the said i-th digit belongs and includes a considerable amount of overlapping portions (that is, portions, which generate the same type of signals overlappingly). If these overlapping portions can be eliminated to an extent not obstructing the high speed of the carry select adder method, it would be possible to simplify the circuit construction and to reduce the number of constituent elements of the circuit. Of course, the two signals of the presumed carry signals C_i(0) and C_i(1) contain redundant information in generating the real sum signals C_i of the digits.

An embodiment of the present invention desirably provides a parallel binary operator using the carry select adder (or subtracter) method, in which binary operator it is possible to cut down on the number of component elements of the circuit without sacrificing high speed.

Figure 4 is a block diagram showing a first embodiment of a binary operator according to the present invention. As shown in Fig. 4, the binary operator embodying the present invention is a binary operator which receives as input two n-bit binary data (A, B). The binary operator has a means (100) which generates a carry propagate signal (P_i) and a carry generate signal (G_i) of various digits, divides the aforementioned two n-bit binary data (A, B) into blocks of predetermined numbers of bits, processes in parallel the blocks of data based on the corresponding aforementioned carry propagate signal (P_i) and carry generate signal (G_i) by a plurality of block adders, calculates the arithmetic sum of the aforementioned two n-bit binary data (A, B), and outputs a real sum signal (F_i), a means (106) for generating a cumulative carry propagate signal (BP_i-1*) from the carry propagate signal (P_M to P_i-1) of the various digits in the aforementioned block adders; a means (107) for generating a cumulative carry generate signal (BG_i-1*) from the carry propagate signal (P_M to P_i-1) and carry generate signals (G_M to G_i-1) of the various digits in the aforementioned block adders; and a means (108) for generating a real sum signal (F_i) by the aforementioned carry propagate signal (P_i), cumulative carry propagate signal (BP_i-1*), cumulative carry generate signal (BG_i-1*), and carry signal (C_M-1) to said block adders.

Figure 5 is a block diagram showing a second embodiment of a binary operator according to the present invention. As shown in Fig. 5, the binary operator embodying the present invention is a binary operator which receives as input two n-bit binary data (A, B), has a means (200) which generates a borrow propagate signal (P_i) and a borrow generate signal (G_i) of various digits, divides the aforementioned two n-bit binary data (A, B) into blocks of predetermined numbers of bits, processes in parallel the blocks of data based on the corresponding aforementioned borrow propagate signal (P_i) and borrow generate signal (G_i) by a plurality of block subtracters, calculates the arithmetic difference of the aforementioned two n-bit binary data (A, B), and outputs a real difference signal (F_i), a means (206) for generating a cumulative borrow propagate signal (BP_i-1*) from the borrow propagate signals (P_M to P_i-1) of the various digits in the aforementioned block subtracters; a means (207) for generating a cumulative borrow generate signal (BG_i-1*) from the borrow propagate signals (P_M to P_i-1) and borrow generate signals (G_M to G_i-1) of the various digits in the aforementioned block subtracters; and means (208) for generating a real difference signal (F_i) by the aforementioned borrow propagate signal (P_i), cumulative borrow propagate signal (BP_i-1*), cumulative borrow generate signal (BG_i-1), and borrow signal (C_M-1) to said block subtracters.

In the parallel full adder shown in Fig. 4, when two n-bit binary data (A, B) are input, a carry propagate signal (P_i) and carry generate signal (G_i) are output from the carry propagate signal and carry generate signal generating means (100). The carry propagate signal (P_i) is applied to the cumulative carry propagate signal generating means (106), the cumulative carry generate signal generating means (107), and the real sum signal generating means (108). At the cumulative carry propagate signal generating means (106), a cumulative carry propagate signal (BP_i*) is generated based on the input carry propagate signals (P_M to P_i) and sent to the real sum signal generating means (108). The carry generate signal (G_i) is given to the cumulative carry generate signal generating means (107). In the cumulative carry generate signal generating means (107), a cumulative carry generate signal (BG_i∗) is generated based on the input carry propagate signals (P_M to P_i) and the carry generate signals (C_M to G_i) and sent to the real sum signal generating means (108). The i-th digit real sum signal generating means (108) generates the real sum signal (F_i) of said digit by four signals: the real carry signal (C_M-1) advanced from the lower digit to the block adder to which it belongs, a carry propagate signal (P_i) of said digit, a cumulative carry propagate signal (BP_i-1*) of the (i-1)-th digit, and a cumulative carry generate signal (BG_i-1*) of the (i-1)-th digit.

That is, in summary, the first embodiment of the present invention does not simultaneously generate two presumed sum signals F_i(0) and F_i(1) and select and output the same as in the above-discussed adder of Fig. 1, but directly performs operations on the three signals P_i , BP_i-1* , and BG_i-1* necessary for generating the presumed sum signal pair F_i(0) and F_i(1) and the real carry signal (C_M-1) to calculate the real sum signal (F_i).

In the parallel full subtracter shown in Fig. 5 when two n-bit binary data (A, B) are input, a borrow propagate signal (P_i) and borrow generate signal (G_i) are output from the borrow propagate signal and borrow generate signal generating means (200). The borrow propagate signal (P_i) is applied to the cumulative borrow propagate signal generating means (206), the cumulative borrow generate signal generating generating means (207), and the real difference signal generating means (208). At the cumulative borrow propagate signal generating means (206), a cumulative borrow propagate signal (BP_i*) is generated based on the input borrow propagate signals (P_M to P_i) and sent to the real difference signal generating means (208). The borrow generate signal (G_i) is given to the cumulative borrow generate signal generating means (207). In the cumulative borrow generate signal generating means (207), a cumulative borrow generate signal (BG_i*) is generated based on the input borrow propagate signals (P_M to P_i) and borrow generate signals (G_M to G_i) and sent to the real difference signal generating means (208). The i-th digit real difference signal generating means (208) generates the real difference signal (F_i) of said digit by four signals: the real borrow signal (C_M-1) advanced from the lower digit to the block subtracter to which it belongs, a borrow propagate signal (P_i) of said digit, a cumulative borrow propagate signal (BP_i-1*) of the (i-1)-th digit, and a cumulative borrow generate signal (BG_i-1*) of the (i-1)-th digit.

That is, in summary, the second embodiment of the present invention does not simultaneously generate two presumed difference signals F_i(0) and F_i(1) and select and output the same as in the above-discussed subtractor, but directly performs operations on the three signals P_i, BP_i-1*, and BG_i-1* necessary for generating the presumed difference signal pair F_i(0) and F_i(1) and the real borrow signal C_M-1 to calculate the real difference signal (F_i).

To standardize the explanation, a circuit construction based on a 64-bit ALU (i.e. the same type as in Fig. 1) is shown in Fig. 6. The explanation will be made based on this.

The CSA circuit 101a, which is a one block adder, simultaneously processes m digit (4 bit) signals. In the CSA circuit 101a, wherein the lowest digit is the M-th digit, the cumulative carry propagate signal BP_i* and the cumulative carry generate signal BG_i* for the i-th digit are defined by the following equations (5) and (6):<maths id="math0006" num=""><img file="EP0347029B1_D0006.tif" /></maths><maths id="math0007" num=""><img file="EP0347029B1_D0007.tif" /></maths>    (where, i = M, M+1, ... , M+m-1)

Here, the cumulative carry propagate signal BP_i* and cumulative carry generate signal BG_i* and the prior block carry propagate signal BP_i and block carry generate signal BG_i are clearly different in the point that the former are signals used in bit units, while the latter are signals used in block units for the BLACG circuits. Therefore, to clearly differentiate the two, the former are used with the symbol "*" attached thereto and expressed as "BP_i*" and "BG_i*".

Next, the i-th digit real sum signal F_i has the following relationship with the real carry signal C_M-1 input to the CSA circuit 101a dealing with the i-th digit and the cumulative carry propagate signal BP_i-1*, cumulative carry generate signal BG_i-1*, and carry propagate signal P_i:<maths id="math0008" num=""><img file="EP0347029B1_D0008.tif" /></maths>

Here, it is defined that BG_M-1* = "0", and BP_M-1* = "1".

That is, from the above-mentioned equation (7), it is understood that the presumed sum signals F_i(0) and F_i(1) can be generated simultaneously from the known signals (P_i , BG_i-1*, and BP_i-1*). Therefore, there is no need for separate generation of the presumed sum signals F_i(0) and F_i(1) as in the adder of Fig. 2. By using the combination of the i-th digit carry propagate signal P_i , the (i-1)-th digit cumulative carry propagate signal BP_i-1*, and the cumulative carry generate signal BG_i-1* and the real carry signal C_M-1 as it is in the CSA circuit, it is possible to generate the i-th digit real sum signal F_i directly.

By doing this, it is possible to eliminate the redundancy in separately generating both the presumed sum signal F_i(0) and F_i(1) and therefore it is possible to delete the circuit required for this generation and thus simplify the circuit construction and cut down on the number of constituent elements of the circuit. By doing so, if the operating time of the circuit for processing the above-mentioned signals P_i , BP_i-1*, and BG_i-1* is less than the operating time for generating the real carry signal, which requires the most time in the operation process, it is possible to realize a parallel full adder having an equivalent processing speed to that of the above-discussed block carry select adder method with fewer circuit constituent elements.

Figure 6 shows a summary of the first embodiment. The point of difference with Fig. 1 lies in the construction of the CSA circuit 101a. The same construction is used for the other input data A, B, ULB circuit 100, BLACG circuit 105, and second MPX circuit 104, so the same symbols are appended and explanations thereof are omitted.

The CSA circuit 101a in the first embodiment differs from the CSA circuit 101 in that it does not generate in parallel the presumed sum signals F_i(0) and F_i(1) but newly introduces the cumulative carry propagate signal BP_i-1* and the cumulative carry generate signal BG_i-1* for each bit and directly calculates the real sum signal F_i.

Next, Fig. 7 shows a first example of the CSA circuit 101a according to the first embodiment. This Fig. 7 shows the example of the CSA circuit 101_a-1 dealing with the first block (input data A₀ to A₃ , B₀ to B₃) in Fig. 6. In Fig. 7 (a) is a symbolized view and (b) is a detailed circuit diagram.

As shown in Fig. 7(b), the CSA circuit 101_a-1 receives as input the carry propagate signals P₀ to P₃ and the carry generate signals G₀ to G₃ corresponding to the bits from ULB circuit 100. As constituent elements of the circuit, use is made of combinations of NAND circuits, NOR circuits, inverter circuits, and EOR circuits using CMOS transistors. Note that use may also be made of bipolar transistors and other digital elements.

As shown in Fig. 7(b), the CSA circuit includes a cumulative carry propagate signal generating unit 106, a cumulative carry generate signal generating unit 107 and a real sum signal generating unit 108. The third digit cumulative carry propagate signal generating unit 106 comprises a four-inputs NAND circuit 161 and an inverter circuit 162. The four inputs of said NAND circuit 161 are supplied with carry propagate signals P₀ to P₃, an output of the NAND circuit 161 is connected to an input of the inverter circuit 162, and the inverter circuit 162 outputs a cumulative carry propagate signal BP₃*.

The third digit cumulative carry generate signal generating unit 107 comprises an inverter circuit 171, a two-input NAND circuit 172, a three-inputs NAND circuit 173 and a first and a second four-input NAND circuits 174 and 175. An input of the inverter circuit 171 is supplied with a carry generate signal G₃ , a first input of the two-inputs NAND circuit 172 is supplied with a carry generate signal G₂ and a second input of the two-inputs NAND circuit 172 is supplied with a carry propagate signal P₃. A first input of the three-input NAND circuit 173 is supplied with a carry generate signal G₁ and a second and a third inputs of the three-input NAND circuit 173 are supplied with carry propagate signals P₂ and P₃. A first input of the first four-input NAND circuit 174 is supplied with a carry generate signal G₀ and a second, a third and a fourth inputs of the first four-input NAND circuit 174 are supplied with carry propagate signals P₁ to P₃. Outputs of the inverter circuit 171, the two-input NAND circuit 172, the three-input NAND circuit 173 and the first four-input NAND circuit 174 are connected to four inputs of the second four-input NAND circuit 175, and the second four-input NAND circuit 175 outputs a cumulative carry generate signal BG₃*.

The real sum signal generating unit 108 comprises a NOR circuit 181 and a first and a second EOR circuits 182 and 183. A first input of the NOR circuit 181 is supplied with an inverted real carry signal <maths id="math0009" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>C</mtext></mrow><mrow><mtext>-1</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0009.tif" /></maths> and a second input of a NOR circuit is supplied with an inverted cumulative carry propagate signal <maths id="math0010" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>BP</mtext></mrow><mrow><mtext>2</mtext></mrow></msub><mtext>*</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0010.tif" /></maths> (<maths id="math0011" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>BP</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><mtext>*</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0011.tif" /></maths>, <maths id="math0012" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>BP</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><mtext>*</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0012.tif" /></maths>). A first input of the first EOR circuit 182 is supplied with a carry propagate signal P₃ (P₂ , P₁) and a second input of the first EOR circuit 182 is supplied with a cumulative carry generate signal BG₂* (BG₁*, BG₀∗), an output of the first EOR circuit 182 is connected to a first input of the second EOR circuit 183 and an output of the NOR circuit 181 is connected to a second input of the second EOR circuit 183, and the second EOR circuit 183 outputs a real sum signal F₃ (F₂ , F₁).

The CSA circuit 101_a-1 is roughly comprised of five parts. In the first part, the real sum signal F₀ is generated by the inverted signal <maths id="math0013" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>C</mtext></mrow><mrow><mtext>-1</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0013.tif" /></maths> of the real carry signal and the carry propagate signal P₀.

Note that C_-1 is a carry signal from the digit below the 0-th digit (lowest digit) and that C_-1 = "0" in the addition of independent binary numbers. Further, the cumulative carry propagate signal BP_M* of the lowest digit (in the case of the present example, the 0-th digit) in the block adder is equal to the M-th digit carry propagate signal P_M from equation (5). Similarly, the M-th digit cumulative carry generate signal BG_M* is equivalent to the M-th digit carry generate signal G_M. The M-th digit real sum signal can be expressed as F_M = P_M ⊕ C_M-1 by making BG_M-1* = "0" and BP_M-1* = "1".

In the second part, the real sum signal F₁ is generated by the inverted signal <maths id="math0014" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>C</mtext></mrow><mrow><mtext>-1</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0014.tif" /></maths> of the real carry signal, the carry propagate signal P1 , the inverted signal <maths id="math0015" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>BP</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><mtext>*</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0015.tif" /></maths> (= <maths id="math0016" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>P</mtext></mrow><mrow><mtext>0</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0016.tif" /></maths>) of the cumulative carry propagate signal, and the cumulative carry generate signal BG₀* (= G₀).

In the third part the real sum signal F₂ is generated by the inverted signal <maths id="math0017" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>C</mtext></mrow><mrow><mtext>-1</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0017.tif" /></maths> of of the real carry signal, the inverted signal <maths id="math0018" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>BP</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><mtext>*</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0018.tif" /></maths> of the cumulative carry propagate signal (generated from P₀ and P₁), the cumulative carry generate signal BG₁* (generated from G₀ , G₁ , and P₁), and the carry propagate signal P₂.

In the fourth part, the real sum signal F₃ is generated by the inverted signal <maths id="math0019" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>C</mtext></mrow><mrow><mtext>-1</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0019.tif" /></maths> of of the real carry signal, the inverted signal <maths id="math0020" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>BP</mtext></mrow><mrow><mtext>2</mtext></mrow></msub><mtext>*</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0020.tif" /></maths> of the cumulative carry propagate signal (generated from P₀ , P₁ , and P₂), the cumulative carry generate signal BG₂* (generated from G₀ , G₁ , G₂ , P₁ , and P₂), and the carry propagate signal P₃.

In the fifth part, the cumulative carry propagate signal BP₃* and the cumulative carry generate signal BG₃* relating to the 3rd bit (that is, the highest digit in the first block) are generated.

As explained above, the real sum signals F₀ , F₁ , F₂ , and F₃ in one block are directly generated without generating in parallel both the presumed sum signals F_i(0) and F_i(1). Therefore, there is no need for the first MPX circuit 102 (Fig. 1). Note that this embodiment of the present invention is similar to the adder of Fig. 1 in that the cumulative carry propagate signal BP₃* and the cumulative carry generate signal BG₃* are input to the BLACG circuit 105 for carry look ahead processing.

Above, the explanation was made with respect to one CSA circuit 101_a-1 , but the same construction applies to a CSA circuit dealing with other blocks, so an explanation thereof is omitted.

According to the first example of the first embodiment, it is possible to cut down seven gates' worth of circuit elements per 4 bits in the portion (CSA circuit 101a) generating the real sum signal F_i. In the overall ALU of Fig. 6, it is possible to reduce the conventional 1152 gates to 1040 gates. Further, the ALU of Fig. 6 has many real carry signal generating circuits (BLACG circuits 105 and second MPX circuits 104), so overall there is only a reduction of about 10 percent, but by applying the same concept as the present invention to these generating circuits, it is possible to reduce them in number to half or less, so in the final analysis it is possible to achieve a reduction of over 20 percent.

Figure 8 shows a first modification of the real sum generating circuit shown in Fig. 7(b). This Fig. 8 shows the portion generating the real sum signal F_i using the real carry signal C_M-1, the carry propagate signal P_i, the cumulative carry propagate signal BP_i-1*, and cumulative carry generate signal BG_i-1*. The other portions are omitted.

As shown in Fig. 8, the real sum signal generating unit 108 comprises an EOR circuit 1811, an ENOR circuit 1812, a first and a second transfer gate circuits 1813 and 1814, and an inverter circuit 1815. A first input of the EOR circuit 1811 is supplied with a cumulative carry propagate signal BP_i-1*, a first input of the ENOR circuit 1812 is supplied with a cumulative carry generate signal BG_i-1*, and a second input of the ENOR circuit 1812 is supplied with a carry propagate signal P_i. An output of the EOR circuit 1811 is connected to an input of the first transfer gate circuit 1813, and an output of the ENOR circuit 1812 is connected to a second input of the EOR circuit 1811 and an input of the second transfer gate circuit 1814. A first control gate of the first transfer gate circuit 1813 and a second control gate of the second transfer gate circuit 1814 are connected and supplied with a real carry signal C_M-1, a second control gate of the first transfer gate circuit 1813 and a first control gate of the second transfer gate circuit 1814 are connected and supplied with an inverted real carry signal C_M-1. Outputs of the first and second transfer gate circuits 1813 and 1814 are commonly connected to an input of the inverter circuit 1815, and the inverter circuit 1815 outputs a real sum signal F_i.

This first modification of the first embodiment generates the inverted signal <maths id="math0021" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>F</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext>(0)</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0021.tif" /></maths> of the presumed sum signal by the ENOR circuit from the carry propagate signal P_i and the cumulative carry generate signal BG_i-1* and generates the inverted signal <maths id="math0022" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>F</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext>(1)</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0022.tif" /></maths> of the presumed sum signal by the EOR circuit from the presumed sum signal <maths id="math0023" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>F</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext>(0)</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0023.tif" /></maths> and the cumulative carry propagate signal BP_i-1*. This circuit selects one of the <maths id="math0024" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>F</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext>(0)</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0024.tif" /></maths> and the <maths id="math0025" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>F</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext>(1)</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0025.tif" /></maths> by the real carry signal C_M-1 to the said CSA circuit 101a by the switch action of the transfer gate TG to obtain the real sum signal F_i.

This circuit is the same as that of Fig. 2 regarding the method of selection of the real carry signal of C_M-1 of either of the presumed sum signals of the case where the carry signal C_M-1 is "0" and where C_M-1 is "1", but differs in that it does not, like in the Fig. 2 method, take the presumed sum signal F_i(1) of the case where C_M-1 is "1" calculated in the equation of F_i(1) = P_i ⊕ C_i-1(1) by using the presumed carry signal C_i-1(1) in the case where C_M-1 is "1". The presumed carry signal C_i-1(0) in the case where the C_M-1 is "0" is equal to the cumulative carry U generate signal BG_i-1*, so the generation of the presumed sum signal F_i(0) is the same as in Fig. 2.

Therefore, the difference in the circuit construction from the circuitry of Fig. 2 lies in the circuit for generating the cumulative carry propagate signal BP_i-1* and the circuit for generating a carry signal C_i-1(1).

According to the above first modification of the first embodiment, considering the number of processing bits per one CSA circuit 101a (m=4), while the present modification requires only three gates for the generation of the cumulative carry propagate signal BP_i-1*, the generation of the carry signal C_i-1(1) in the prior art requires as many as eight gates. In the present embodiment, it is possible to immediately obtain the real sum signal F_i by the selection operation by the real carry signal C_M-1 , so it is possible to have the same high speed processing as in the above-discussed example of Figs 1 to 3.

Note that in general the carry propagate signal P_i and the carry generate signal G_i do not become "1" simultaneously. Using the fact that BP_i* and BG_i* do not simultaneously become "1", from equations (5) and (6), equation (7) is modified to the following to construct a logical circuit:<maths id="math0026" num=""><img file="EP0347029B1_D0026.tif" /></maths>

Figure 9 shows a second modification of the first embodiment. Figure 9 shows only the important portions in the same way as Fig. 8.

As shown in Fig. 9, the real sum signal generating unit 108 comprises a NOR circuit 1821, an inverter circuit 1822, a first and a second transfer gate circuits 1823 and 1824, and an ENOR circuit 1825. A first input of the NOR circuit 1821 is supplied with a cumulative carry propagate signal BP_i-1*, a second input of the NOR circuit 1821 and an input of the inverter circuit 1822 are connected and supplied with a cumulative carry generate signal BG_i-1*. An output of the NOR circuit 1821 is connected to an input of the first transfer gate circuit 1823, and an output of the inverter circuit 1822 is connected to an input of the second transfer gate circuit 1824. A first control gate of the first transfer gate circuit 1823 and a second control gate of the second transfer gate circuit 1824 are connected and supplied with a real carry signal C_M-1 , a second control gate of the first transfer gate circuit 1823 and a first control gate of the second transfer gate circuit 1824 are connected and supplied with an inverted real carry signal <maths id="math0027" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>C</mtext></mrow><mrow><mtext>M-1</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0027.tif" /></maths>. Outputs of the first and second transfer gate circuits 1823 and 1824 are commonly connected to a first input of the ENOR circuit 1825 and a second input of the ENOR circuit 1825 is supplied with a carry propagate signal P_i , and the ENOR circuit 1825 outputs a real sum signal F_i.

This second modification of the first embodiment taken note of the fact that the presumed sum signal F_i(0) and F_i(1) are generated by taking the EOR of the carry propagate signal P_i and the cumulative carry generate signal <maths id="math0028" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>BG</mtext></mrow><mrow><mtext>i-1</mtext></mrow></msub><mtext>*</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0028.tif" /></maths> and (<maths id="math0029" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>BG</mtext></mrow><mrow><mtext>i-1</mtext></mrow></msub><msub><mrow><mtext>* + BP</mtext></mrow><mrow><mtext>i-1</mtext></mrow></msub><mtext>*</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0029.tif" /></maths>), first selects one of the BG_i-1* and (BG_i-1* + BP_i-1*) by the real carry signal C_M-1*, then takes the ENOR of the selected signal and P_i and generates the true sum signal F_i.

According to the second modification of the first embodiment, it is possible to save 1.5 gates per digit compared with the first modification (Fig. 8). However, from the standpoint of the operation speed, since not only a selector (transfer gate), but also an ENOR circuit are interposed after the generation of the real carry signal C_M-1 , the delay time contributes to the delay time in the worst case and the operation is delayed by that amount. However, in the case of a 1 to 1.5 µm CMOS, the delay time in the worst case required for 64-bit full addition is 15 to 20 nsec in the construction of the first modification of the first embodiment (Fig. 8), while the delay time of one EOR or ENOR stage of the present modification is about 1 nsec, which is not a critical defect for a high speed adder.

Figure 10 shows a third modification of the first embodiment. Figure 10 shows only the important portions in the same way as Fig. 8.

As shown in Fig. 10, the real sum signal generating unit 108 comprises an AND circuit 1831, a NOR circuit 1832 and an ENOR circuit 1833. A first input of the AND circuit 1831 is supplied with a cumulative carry propagate signal BP_i-1*, a second input of said AND circuit is supplied with a real carry signal C_M-1 , and an output of the AND circuit 1831 is connected to a first input of the NOR circuit 1832, a second input of the NOR circuit 1832 is supplied with a cumulative carry generate signal BG_i-1*. A first input of the ENOR circuit 1833 is supplied with a carry propagate signal P_i and an output of the NOR circuit 1832 is connected to a second input of the ENOR circuit 1833, and the ENOR circuit 1833 outputs a real sum signal F_i.

The third modification of the first embodiment shows an example of the case of modification of equation (7) as shown by the following equation (9):<maths id="math0030" num="(9)"><math display="block"><mrow><msub><mrow><mtext>F</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext> = </mtext><mover accent="true"><mrow><msub><mrow><mtext>P</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext> ⊕ (</mtext><mover accent="true"><mrow><msub><mrow><mtext>BG</mtext></mrow><mrow><mtext>i-1</mtext></mrow></msub><msub><mrow><mtext>* + BP</mtext></mrow><mrow><mtext>i-1</mtext></mrow></msub><msub><mrow><mtext>* · C</mtext></mrow><mrow><mtext>M-1</mtext></mrow></msub></mrow><mo>¯</mo></mover><mtext>)</mtext></mrow><mo>¯</mo></mover><mspace linebreak="newline" /><msub><mrow><mtext> = P</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext> ⊕ (BG</mtext></mrow><mrow><mtext>i-1</mtext></mrow></msub><msub><mrow><mtext>* + BP</mtext></mrow><mrow><mtext>i-1</mtext></mrow></msub><msub><mrow><mtext>* · C</mtext></mrow><mrow><mtext>M-1</mtext></mrow></msub><mtext>)</mtext></mrow></math><img file="EP0347029B1_D0030.tif" /></maths>

According to the third modification of the first embodiment, in circuit construction, it is possible to further cut one gate per digit compared with the second modification (Fig. 9). While the third modification is somewhat slower from the standpoint of the operation speed, the difference is at the most 1 nsec or so, which does not pose a problem in practice.

Figure 11 shows a fourth modification of the first embodiment. Figure 11 shows just the important portions in the same way as Fig. 8.

As shown in Fig. 11, the real sum signal generating unit 108 comprises a NAND circuit 1841, an EOR circuit 1842 and an ENOR circuit 1843. A first input of the NAND circuit 1841 is supplied with a real carry signal C_M-1 and a second input of the NAND circuit 1841 is supplied with a cumulative carry propagate signal BP_i-1*. A first input of the EOR circuit 1842 is supplied with a cumulative carry generate signal BG_i-1* and a second input of the EOR circuit 1842 is supplied with a carry propagate signal P_i. An output of the NAND circuit is connected to a first input of the ENOR circuit 1843 and an output of the EOR circuit 1842 is connected to a second input of the ENOR circuit 1843, and the ENOR circuit 1843 outputs a real sum signal F_i.

The fourth modification of the first embodiment shows an example of the case of modification of equation (9) to the following:<maths id="math0031" num="(10)"><math display="block"><mrow><msub><mrow><mtext>F</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext> = P</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext> ⊕ BG</mtext></mrow><mrow><mtext>i-1</mtext></mrow></msub><mtext>* ⊕ </mtext><mover accent="true"><mrow><msub><mrow><mtext>BP</mtext></mrow><mrow><mtext>i-1</mtext></mrow></msub><msub><mrow><mtext>* · C</mtext></mrow><mrow><mtext>M-1</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0031.tif" /></maths>

According to the fourth modification of the first embodiment, in circuit construction, there is an increase of one gate compared with the second modification (Fig. 9), but the fourth modification is somewhat faster from the standpoint of the operation speed (difference of 0.5 nsec or less).

Note that the circuit of the fourth modification of the first embodiment is substantially the same as that used in the broken line portion shown in the first embodiment (Fig. 7).

Figure 12 shows a fifth modification of the first embodiment. Figure 12 shows only the important portions in the same way as Fig. 8.

As shown in Fig. 12, the real sum signal generating unit 108 comprises a NAND circuit 1851, an EOR circuit 1852, a first, a second and a third inverter circuits 1853, 1854 and 1855,and a first and a second transfer gate circuits 1856 and 1857. A first input of the NAND circuit 1851 is supplied with a real carry signal C_M-1 and a second input of a NAND circuit 1851 is supplied with a cumulative carry propagate signal BP_i-1*. A first input of the EOR circuit 1852 is supplied with a cumulative carry generate signal BG_i-1* and a second input of the EOR circuit 1852 is supplied with a carry propagate signal P_i. An output of the NAND circuit 1851 is commonly connected to an input of the first inverter circuit 1853, a second control gate of the first transfer gate circuit 1856 and a first control gate of the second transfer gate circuit 1857. An output of the EOR circuit 1852 is commonly connected to an input of the second inverter circuit 1854 and an input of the first transfer gate circuit 1856. An output of the first inverter circuit 1853 is commonly connected to a first control gate of the first transfer gate circuit 1856 and a second control gate of the second transfer gate circuit 1857. An output of the second inverter circuit 1854 is connected to an input of the second transfer gate circuit 1857, outputs of the first and second transfer gate circuits 1856 and 1857 are commonly connected to an input of the third inverter circuit 1855, and the third inverter circuit 1855 outputs a real sum signal F_i.

The fifth modification of the first embodiment is substantially the same circuit as the circuit of the fourth modification (Fig. 11) except that the ENOR circuit for obtaining the real sum signal F_i is changed to a transfer gate TG (selector).

According to the fifth modification of the first embodiment, in circuit construction, the number of elements is the same as in Fig. 11 and the operation speed is somewhat faster.

Above, according to the first to fifth modifications of the first embodiment of the present invention shown in Fig. 8 to Fig. 12, no matter what circuit constructions are employed, it is possible to construct a parallel full adder having about the same processing speed as in the example of Fig. 1 with fewer elements than in the construction of Fig. 1. The elements are reduced most in the case of the construction of Fig. 10, but the time required for generation of the real sum signal F_i after the generation of the real carry signal C_M-1 is longer compared with the other circuits, so application is suitably for circuit portions not requiring relatively high speeds. The circuit of Fig. 8 is higher in speed than the other circuits, but the number of elements is greater, so application is desirably to CSA circuits where time is taken for generation of the real carry signal C_M-1.

Further, when the data length is long, such as in a 64-bit full adder, for the carry processing of the ALU of Fig. 6, the output signal of the second MPX circuit 104 is transmitted to the higher digits by the ripple carry method, so the time required for generating the real carry signal C_M-1 is longer in the case of a higher digit than a lower digit. Therefore, by utilizing this time difference and using the circuit of Fig. 10 in the CSA circuit 101a at the lower digits (for example, the 0th to 47th digits) and using the circuit of Fig. 8 or Fig. 12 in the CSA circuit 101a of the higher digits (for example, 48th to 63rd digits), it is possible to cut down on the overall number of circuit elements without increasing the delay time in the worst case.

Figure 13 shows a second example of the CSA circuit according to the first embodiment. Figure 13(a) shows a symbolized view of the CSA circuit 101b of the present embodiment and Fig. 13(b) shows a detailed circuit diagram of the same.

While the CSA circuits 101a shown in Figs. 7 to 12 were constructed of NAND, NOR, inverter, EOR and ENOR circuits using CMOS transistors, the CSA circuit 101b of the second example replaces most of these with chain circuits of the wired OR circuits of transfer gates TG and inverter circuits INV to secure equivalent functions as with the CSA circuits 101a.

The construction will be explained next. The CSA circuit 101b roughly comprises of six parts.

The first part is a circuit 106 for generating the cumulative carry propagate signal BP_i*. Here, the cumulative carry propagate signal BP_i* is given by:<maths id="math0032" num=""><img file="EP0347029B1_D0032.tif" /></maths>    (where, i = 0, 1, 2, 3) This BP_i* generating circuit 106 gives the carry propagate signal P₀ of the 0-th digit (smallest digit) held within the CSA circuit 101b to the input terminal of the chain circuit of the transfer gate circuit TG for each stage, controls the ON-OFF state of the transfer gate circuit TG dealing with the digits (i = 0, 1, 2, 3) by the carry propagate signal P_i of said digits, generates a signal corresponding to "0" in the digit where the transfer gate circuit TG becomes OFF, and successively conveys it to the higher digits.

As shown in Fig. 13(b), the cumulative carry propagate signal generating unit 106, the cumulative carry generate signal generating unit 107 and the real sum signal generating unit 108 comprise a chain circuit mutually connected with a transfer gate circuit and an inverter circuit.

The conveyed signal is inverted with each stage of the inverter circuits passed through, so the circuit is comprised so that by the generation of the above-mentioned "0" corresponding signal, a "0" corresponding signal is conveyed to the higher digits at digits where a noninverted signal of the cumulative carry propagate signal BP_i* is conveyed and a "1" corresponding signal is conveyed at digits where the inverted signal of the cumulative carry propagate signal BP_i* is conveyed. Together with the polarity of the cumulative carry propagate signal BP_i*, the circuits generating the cumulative carry propagate signal BP_i' adjusted by the carry signal C_-1 may be used differentiated as to NAND and NOR types. Here, BP_i' is given by:<maths id="math0033" num="(11)"><math display="block"><mrow><msub><mrow><mtext>BP</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext>' = BP</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext>*·C</mtext></mrow><mrow><mtext>-1</mtext></mrow></msub></mrow></math><img file="EP0347029B1_D0033.tif" /></maths>

In this way, the BP_i* generating circuit 106 receives as input the carry propagate signals P_i , <maths id="math0034" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>P</mtext></mrow><mrow><mtext>i</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0034.tif" /></maths> and the carry signal C_-1 of the digits and generates the cumulative carry propagate signal BP_i* , BP_i', and <maths id="math0035" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>BP</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext>'</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0035.tif" /></maths>. The signals BP_i' and <maths id="math0036" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>BP</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext>'</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0036.tif" /></maths> are used as input signals of the later mentioned real sum signal generating circuits.

The logic "0" corresponding signal generated here is sent to the chain circuit through the MOS transistor MOST. At the digits where the signal on the chain circuit sent to the digit (that is, the cumulative carry propagate signal BP_i*) is sent noninverted through the n-type MOST, the "0" signal (V_SS potential) is generated at the said node of the chain circuit and at the digits where BP_i* is sent inverted, the "1" signal (V_DD potential) is generated through the p-type MOST.

The outputs at the digits of the BP_i* generating circuit (chain circuit) are used for the generation of the i-th digit signal<maths id="math0037" num=""><math display="block"><mrow><msub><mrow><mtext>BP</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext>' = BP</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext>*·C</mtext></mrow><mrow><mtext>M-1</mtext></mrow></msub></mrow></math><img file="EP0347029B1_D0037.tif" /></maths> and its inverted signal together with the real carry signal C_M-1 from the lower digit. The signal BP_i' becomes the input signal of the circuit 108 for generating the i-th digit real sum signal F_i using the relationship of:<maths id="math0038" num=""><math display="block"><mrow><msub><mrow><mtext>F</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext> = P</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext> ⊕ BG</mtext></mrow><mrow><mtext>i-1</mtext></mrow></msub><msub><mrow><mtext> *⊕ BP'</mtext></mrow><mrow><mtext>i-1</mtext></mrow></msub></mrow></math><img file="EP0347029B1_D0038.tif" /></maths>

The second part is the circuit 107 for generating the cumulative carry generate signal BG_i*. Here, the cumulative carry generate signal BG_i* is given by:<maths id="math0039" num=""><img file="EP0347029B1_D0039.tif" /></maths> This BG_i* generating circuit 107 is also comprised of a chain circuit of an inverter circuit INV and a transfer gate circuit TG in the same way as the above-mentioned BP_i* generating circuit 106. The BG_i* generating circuit 107 also controls the ON-OFF state of the transfer gate circuit TG of the digits by the carry propagate signal P_i (P₀ , P₁ , P₂ , and P₃) for each digit. At the digits where the transfer gate circuit TG becomes OFF, a signal corresponding to the carry generate signal G_i (G₀ , G₁ , G₂ , and G₃) is generated at the transfer gate dealing with the digit and successively conveyed to the higher digits. The signal corresponding to the carry generate signal G_i generated here becomes G_i at the digits where the signal sent to that digit (that is, the cumulative carry generate signal BG_i*) is sent noninverted and is <maths id="math0040" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>G</mtext></mrow><mrow><mtext>i</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0040.tif" /></maths> at the digits where BG_i* is sent inverted.

In this way, the BG_i* generating circuit 107 receives as input the carry propagate signal P_i and the carry generate signal G_i of the digits and generates the cumulative carry generate signal BG_i*, <maths id="math0041" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>BG</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext>*</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0041.tif" /></maths> and the inverted signal <maths id="math0042" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>P</mtext></mrow><mrow><mtext>i</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0042.tif" /></maths> of the carry generate signal P_i.

BG_i* and <maths id="math0043" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>BG</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext>*</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0043.tif" /></maths> are used as input signals of the later mentioned real sum signal generating circuits 108. <maths id="math0044" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>P</mtext></mrow><mrow><mtext>i</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0044.tif" /></maths> is used as the input signal of the BP_i* generating circuit 106 and the real sum signal generating circuit 108.

The third part is a circuit for generating the real sum signal F₀ of the 0-th digit (lowest digit in the block), the fourth part is a circuit for generating the real sum signal F₁ of the first digit, the fifth part is a circuit for generating the real sum signal F₂ of the second digit, and the sixth part is a circuit for generating the real sum signal F₃ of the third digit (highest digit in the block). The real sum signal generating circuits output the real sum signals F_i based on the carry propagate signals <maths id="math0045" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>P</mtext></mrow><mrow><mtext>i</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0045.tif" /></maths> , P_i , BP'_i-1, <maths id="math0046" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>BP'</mtext></mrow><mrow><mtext>i-1</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0046.tif" /></maths> , and the cumulative carry generate signals BG_i-1*, <maths id="math0047" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>BG</mtext></mrow><mrow><mtext>i-1</mtext></mrow></msub><mtext>*</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0047.tif" /></maths> of the corresponding digits.

Note that in Fig. 13(b), the inverter INV is inserted for each stage of the transfer gates TG, but that the circuit may be comprised with it inserted with every two or three stages or combined with the same.

According to the second example of the first embodiment, it is possible to cut down on 10 gates' worth of elements compared with the CSA circuits, 101a shown in Figs. 7 to 12 and further it is possible to reduce the number of elements to about 64 percent of a circuit of a combination of the CSA circuit 101 and first MPX circuit 102. In this way, by making the cumulative carry propagate signal BP_i* and the cumulative carry generate signal BG_i* generated by the chain of the transfer gate TG and the inverter INV and, further, by making the circuits for generating the real sum signal F_i , that is, the EOR circuit and ENOR circuits, also comprises of combinations of transfer gates TG and inverters INV, it is possible to considerably reduce the number of the elements while maintaining an equivalent adding speed as in the example of Fig. 1. Further, by optimizing the construction, there is the possibility of achieving a higher speed of operation.

The above-mentioned first and second examples, and first to fifth modification of the first embodiments show examples of parallel full adders, but the present invention can also be applied,in a second embodiment, to parallel full subtracters (not illustrated).

In the second embodiment of a parallel full subtracter using A as the minuend and B as the subtrahend, the carry propagate signal P_i as spoken of in the case of an adder becomes a "borrow propagate signal" and the carry generate signal G_i becomes a "borrow generate signal". The borrow propagate signal P_i in this case is given by the ENOR of<maths id="math0048" num="(3)'"><math display="block"><mrow><msub><mrow><mtext>P</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext> = </mtext><mover accent="true"><mrow><msub><mrow><mtext>A</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext> ⊕ B</mtext></mrow><mrow><mtext>i</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0048.tif" /></maths> Further, the borrow generate signal G_i is given by<maths id="math0049" num="(4)'"><math display="block"><mrow><msub><mrow><mtext>G</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext> = </mtext><mover accent="true"><mrow><msub><mrow><mtext>A</mtext></mrow><mrow><mtext>i</mtext></mrow></msub></mrow><mo>¯</mo></mover><msub><mrow><mtext> · B</mtext></mrow><mrow><mtext>i</mtext></mrow></msub></mrow></math><img file="EP0347029B1_D0049.tif" /></maths> Further, the cumulative carry propagate signal BP_i* is used as the "cumulative borrow propagate signal" and the cumulative carry generate BG_i* is used as the "cumulative borrow generate signal" and, in addition, the carry signal C_M-1 is used as the "borrow signal C_M-1" and the operation is performed successively from the lowest digit (in the case of 64 bits, the 0-th digit) to the highest digit (63-rd digit). With such a signal setting, it is possible to construct a parallel full subtracter using the circuits shown in Figs. 7 to 13 and obtain the real difference signal F_i corresponding to an inverted signal of the real sum signal F_i in those circuits. Therefore, a detailed explanation will be omitted.

Figure 14 is a block diagram showing a third embodiment of a binary operator according to the present invention. As shown in Fig. 14, the parallel full adder, or binary operator, embodying the present invention is a binary operator which receives as input two pieces of n-bit binary data (A, B) and is provided with a means (101) which divides the aforementioned two pieces of n-bit binary data (A,B) into blocks of predetermined number of bits, and is provided with a means (100) which generates a carry propagate signal (Pi) and a carry generate signal (Gi) of various digits, engages in parallel processing based on the aforementioned carry propagate signal (P_i) and carry generate signal (G_i) corresponding to the blocks of data and a real carry signal (C_M-1), and thus calculates the arithmetic sum of the aforementioned two pieces of n-bit binary data (A, B) and generates a real sum signal (F_i), and a means (103) which generates a block carry propagate signal (BP_i) and a block carry generate signal (BG_i) corresponding to the above-mentioned blocks based on the above-mentioned carry propagate signal (P_i) and the carry generate signal (G_i), which is provided with a means (116) for generating a cumulative block carry propagate signal (CP_M-1*) and cumulative block carry generate signal (CG_M-1*) based on the above-mentioned block carry propagate signals (BP_M, - BP_M-1) and block carry generate signals (BG_M, to BG_M-1) and a means (117) for generating a real carry signal (C_M-1) from the above-mentioned cumulative block carry propagate signal (CP_M-1*), cumulative block carry generate signal (CG_M-1), and the carry signal (C_M'-m') to the said block.

Figure 15 is a block diagram showing a fourth embodiment of a binary operator according to the present invention. As shown in Fig. 15, the parallel full subtracter, or binary operator, embodying the present invention, is a binary operator which receives as input two pieces of n-bit binary data (A, B), is provided with a means (201) which divides the aforementioned two pieces of n-bit binary data (A,B) into blocks of predetermined number of bits, and is provided with a means (200) which generates a carry propagate signal (Pi) and a carry generate signal (Gi) of various digits, engages in parallel processing based on the aforementioned borrow propagate signal (P_i) and borrow generate signal (G_i) corresponding to the blocks of data and a real borrow signal (C_M-1), and thus calculates the arithmetic difference of the aforementioned two pieces of n-bit binary data (A, B) and generates a real difference signal (F_i), and a means (203) which generates a block borrow propagates signal (BP_i) and a block borrow generate signal (BG_i) corresponding to the above-mentioned blocks based on the above-mentioned borrow propagate signal (P_i) and the borrow generate signal (G_i), which is provided with a means (216) for generating a cumulative block borrow propagate signal (CP_M-1*) and cumulative block borrow generate signal (CG_M-1*) based on the above-mentioned block borrow propagate signals (BP_M, to BP_M-1) and block borrow generate signals (BG_M, to BG_M-1) and a means (217) for generating a real borrow signal (C_M-1) from the above-mentioned cumulative block borrow propagate signal (CP_M-1*), cumulative block borrow generate signal (CG_M-1*), and the borrow signal (C_M'-m') to the said block.

In the parallel full adder shown in Fig. 14, when two pieces of n-bit binary data (A, B) are input, a carry propagate signal (P_i) and carry generate signal (G_i) are output from the carry propagate signal and carry generate signal generating means (100).

The carry propagate signal (P_i) and the carry generate signal (G_i) are respectively applied to a block addition means (101) and to a block carry propagate signal and block carry generate signal generating means (103).

At the block addition means (101), presumed sum signals F_i(0) and F_i(1) are generated based on the input carry propagate signal (P_i) and carry generate signal (G_i). The presumed sum signal F_i(0) is the signal which is generated in advance envisioning the case of the carry signal from the lower block (C_M-1) being "0" and the presumed sum signal F_i(1) that in the case of the carry signal (C_M-1) being "1".

In the block carry propagate signal and block carry generate signal generating means (103), the block carry propagate signal (BP_i) and the block carry generate signal (BG_i) corresponding to the block addition means (101) are generated based on the carry propagate signal (P_i) and the carry generate signal (G_i) and are output to the cumulative block carry propagate signal and cumulative block carry generate signal generating means 116.

The cumulative block carry propagate signal and cumulative block carry generate signal generating means (116) generates the cumulative block carry propagate signal (CP_M-1*) and cumulative block carry generate signal (CG_M-1*) and outputs them to the real carry signal generating means (117).

The real carry signal generating means (117) generates the real carry signal (C_M-1) based on the cumulative block carry propagate signal (CP_M-1*), cumulative block carry generate signal (CG_M-1*), and the carry signal (C_M'-m') from the lower block and sends it to the above-mentioned block addition means (101) as the selection signal for the pregenerated presumed sum signals F_i(0) or F_i(1).

Next, the block addition means (101) selects one of the presumed sum signals F_i(0) or F_i(1) in accordance with the content of the above-mentioned real carry signal (C_M-1) and outputs the selected sum signal as the real sum signal (F_i).

In summary, the third embodiment of the present invention does not simultaneously generate two presumed carry signals C_i(0) and C_i(1) and select and output the same as discussed with reference to Figs. 1 to 3,but uses the CP_M-1*, CG_M-1* and real carry signal (C_M'-m') to directly generate the real carry signal (C_M-1).

In the parallel full subtracter shown in Fig. 15, when two pieces of n-bit binary data (A, B) are input, a borrow propagate signal (P_i) and borrow generate signal (G_i) are output from the borrow propagate signal and borrow generate signal generating means (200).

The borrow propagate signal (P_i) and the borrow generate signal (G_i) are respectively applied to a block subtraction means (201) and to a block borrow propagate signal and block borrow generate signal generating means (203).

At the block subtraction means (201), presumed difference signals F_i(0) and F_i(1) are generated based on the input borrow propagate signal (P_i) and borrow generate signal (G_i). The presumed difference signal F_i(0) is the signal which is generated in advance envisioning the case of the borrow signal from the lower block (C_M-1) being "0" and the presumed difference signal F_i(1) that in the case of the borrow signal (C_M-1) being "1".

In the block borrow propagate signal and block borrow generate signal generating means (203), the block borrow propagate signal (BP_i) and the block borrow generate signal (BG_i) corresponding to the block subtraction means (201) are generated based on the borrow propagate signal (P_i) and the borrow generate signal (G_i) and are output to the cumulative block borrow propagate signal and cumulative block borrow generate generating means (216).

The cumulative block borrow propagate signal and cumulative block borrow generate signal generating means (216) generates the cumulative block borrow propagate signal (CP_M-1*) and cumulative block borrow generate signal (CG_M-1*) and outputs them to the real borrow signal generating means (217).

The real borrow signal generating means (217) generates the real borrow signal (C_M-1) based on the cumulative block borrow propagate signal (CP_M-1*), cumulative block borrow generate signal (CG_M-1*), and the borrow signal (C_M'-m') from the lower block and sends it to the above-mentioned block subtraction means (201) as the selection signal for the pregenerated presumed difference signals F_i(0) or F_i(1).

Next, the block subtraction means (201) selects one of the presumed difference signals F_i(0) or F_i(1) in accordance with the content of the above-mentioned real borrow signal (C_M-1) and outputs the selected difference signal as the real difference signal (F_i).

In summary, the fourth embodiment of the present invention does not simultaneously generate two presumed borrow signals C_i(0) and C_i(1) and select and output the same as discussed with reference to Figs. 1 to 3 but uses the CP_M-1*, CG_M-1*, and real borrow signal (C_M'-m') to directly generate the real borrow signal (C_M-1).

To standardize the explanation, a circuit construction based on a 64-bit ALU (Fig. 1) is shown in Fig. 16. The explanation will be made based on this.

The CSA circuit 101, which is one block adder, is made one which simultaneously processes m digit (4 bit) signals. In the CSA circuit 101, wherein the lowest digit is the M-th digit, the block carry propagate signal BP_i and the block carry generate signal BG_i for the i-th digit are defined by the following equations (15) and (16).<maths id="math0050" num=""><img file="EP0347029B1_D0050.tif" /></maths><maths id="math0051" num=""><img file="EP0347029B1_D0051.tif" /></maths>    (where, i = M + m - 1, M = 0, m, 2m, 3m ...)

The CSA circuit 101 having the M-th digit as the lowest digit generates the block carry propagate signal BP_i and the block carry generate signal BG_i given by the above-mentioned equations (15) and (16) and also generates the presumed sum signals F_i′(0) and F_i'(1). Here, the "i'" in the F_i'(0) and F_i′(1) equals M, M + 1, ... M + m - 1, (M = 0, m, 2m, 3m, ...)

On the other hand, the BLACG circuit 105 divides the block carry propagate signal BP_i and block carry generate signal BG_i generated in the above way into q digits and processes the same as such. In the BLACG circuit 105 having the M'-th digit as the lowest digit, the cumulative block carry propagate signal CP_i* and the cumulative block carry generate signal CG_i* are defined by the following equations (17) and (18):<maths id="math0052" num=""><img file="EP0347029B1_D0052.tif" /></maths><maths id="math0053" num=""><img file="EP0347029B1_D0053.tif" /></maths>    (where, i = M', M' + m, M' + 2m, ... ,)<maths id="math0054" num=""><math display="block"><mrow><mtext>M' + (q-1)·m</mtext></mrow></math><img file="EP0347029B1_D0054.tif" /></maths><maths id="math0055" num=""><math display="block"><mrow><mtext>I = (i-M')/m, M' = (kq+1)m-1</mtext></mrow></math><img file="EP0347029B1_D0055.tif" /></maths> (k is an integer of 0 or more).

The cumulative block carry propagate signal CP_i* and cumulative block carry generate signal CG_i* and the real carry signal C_M'-m' (carry signal from the lower block) to the said BLACG circuit 105 have the following relationship (19) with the i-th digit real carry signal C_i:<maths id="math0056" num="(19)"><math display="block"><mrow><msub><mrow><mtext>C</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext> = CG</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext>* + CP</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext>* · C</mtext></mrow><mrow><mtext>M'-m'</mtext></mrow></msub></mrow></math><img file="EP0347029B1_D0056.tif" /></maths>

In this way, the circuit does not generate the presumed carry signals C_i(0) and C_i(1) in advance and select and output one of the same by the carry signal C_M'-m' , but directly generates the i-th digit real carry signal C_i by just the cumulative block carry propagate signal CP_i* and cumulative block carry generate signal CG_i* given by equations (17) and (18) and the carry signal C_M'-m' to the BLACG circuit of the block. By this, it is possible to eliminate the redundant circuits mentioned above and it is possible to simplify the circuit. At this time, by giving consideration to minimize the time required from the time when the carry signal C_M'-m' is input to the time when the real carry signal C_i is generated (that is, the delay time), it is possible to simplify the circuit and to maintain the high speed.

Figure 16 shows a summary of the third embodiment. The point of difference with the circuitry of Fig. 1 lies in the construction of the BLACG circuit 105a. The same construction is used for the other input data A, B, ULB circuit 100, CSA circuit 101, and first MPX circuit 102, so the same symbols are appended and explanations thereof are omitted.

The BLACG circuit 105a in the third embodiment differs from the conventional BLACG circuit 105 in the point that it does not generate in parallel the presumed carry signals C_i(0) and C_i(1) but newly introduces the cumulative block carry propagate signal CP_i* and the cumulative block carry generate signal CG_i* for each bit and directly calculates the real carry signal C_i.

Next, Fig. 17 shows a first example of the BLACG circuit 105a according to the third embodiment. This Fig. 17 shows the example of the BLACG circuit 105_a-1 dealing with the first block in Fig. 16. In Fig. 17, (a) is a symbolized view and (b) is a detailed circuit diagram.

As shown in Fig. 17(b), the real carry signal generating unit 117 comprises a NOR circuit 1171, a first and a second inverter circuits 1172 and 1173, and a first and a second transfer gate circuits 1174 and 1175. An input of the first inverter circuit 1172 and a first input of the NOR circuit 1171 are connected and supplied with a cumulative block carry generate signal CG₁₅* (CG₁₁*, CG₇*, or a block carry generate signal BG₃), a second input of the NOR circuit 1171 is supplied with a cumulative block carry propagate signal CP₁₅* (CP₁₁*, CP₇*, or a block carry propagate signal BP₃). An output of the first inverter circuit 1172 is connected to an input of the first transfer gate circuit 1174 and an output of the NOR circuit 1171 is connected to an input of the second transfer gate circuit 1175. A first control gate of the first transfer gate circuit 1174 and a second control gate of the second transfer gate circuit 1175 are connected and supplied with an inverted real carry signal <maths id="math0057" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>C'</mtext></mrow><mrow><mtext>-1</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0057.tif" /></maths> , a second control gate of the first transfer gate circuit 1174 and a first control gate of the second transfer gate circuit 1175 are connected and supplied with a real carry signal C'_-1. Outputs of the first and second transfer gate circuits 1174 and 1175 are commonly connected to an input of the second inverter circuit 1173, and the second inverter circuit 1173 outputs a real carry signal C₁₅ (C₁₁ , C₇ , C₃).

As shown in Fig. 17(b), the BLACG circuit 105_a-1 receives as input the block carry propagate or generate signals BP₀ , BG₃ to BP₁₅ , BG₁₅ from the CSA circuit 101, and the carry signal C_-1. As constituent elements of the circuit, use is made of combinations of NAND circuits, inverter circuits, NOR circuits, and EOR circuits using CMOS transistors. Note that use may also be made of bipolar transistors and other digital elements.

As to the question of how many circuit elements are required for generation of the real carry signal C_i by application of the present invention compared with the example of Figs. 1 to 3 and what happens to the processing speed, it is necessary to consider also the circuits for generating the cumulative block carry propagate signal CP_i* and the cumulative block carry generate signal CG_i*.

Therefore, the first example of the third embodiment (Fig. 17) is constructed using a circuit which generates the cumulative block carry propagate signal CP_i* and the cumulative block carry generate signal CG_i* by about the same procedure as the circuit of Fig. 3 and which is made by a later mentioned second modification of the third embodiment (Fig. 19).

This BLACG circuit 105_a-1 is roughly comprised of five blocks. In the first block, the second carry signals C'_-1 and <maths id="math0058" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>C'</mtext></mrow><mrow><mtext>-1</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0058.tif" /></maths> are generated by the carry signal C_-1 from the lower block.

In the second block, the cumulative block carry propagate signal CP₃* and the cumulative block carry generate signal CG₃* are generated based on the block carry propagate signal BP₃ and the block carry generate signal BG₃ and the real carry signal C₃ for the third digit is generated from the CP₃*, CG₃*, and second carry signals C'_-1 and' <maths id="math0059" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>C'</mtext></mrow><mrow><mtext>-1</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0059.tif" /></maths>.

Below, in the same way, in the third block, the cumulative block carry propagate signal and the cumulative block carry generate signal are generated from the corresponding block carry propagate signal and block carry generate signal and the real carry signal C₇ for the seventh digit is generated from the second carry signals C'_-1 and <maths id="math0060" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>C'</mtext></mrow><mrow><mtext>-1</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0060.tif" /></maths>. Similarly, in the fourth block, the real carry signal C₁₁ and in the fifth block the real carry signal C₁₅ are respectively generated.

In this way, the real carry signals C₃ , C₇ , C₁₁ , and C₁₅ in one block are directly generated without parallel generation of the presumed carry signals C_i(0) and C_i(1). Therefore, there is no need for the second MPX circuit 104 as in the prior art.

The above BLACG circuit 105a has a total of 132 circuit elements, which is 4 elements less than the 136 of the conventional circuit (Fig. 3, total of BLACG circuit 105 and second MPX circuit 104). Further, the five-input NAND circuit used for generating the carry signal C₁₅(1) in the circuit of Fig. 3 is comprised of an inverter and two-input NOR in the present embodiment, so it is possible to generate the real carry signal C₁₅ faster and to also improve the overall addition speed.

The above explanation was made with reference to a single BLACG circuit 105_a-1 , but the same construction applies to a BLACG circuit dealing with other blocks, so an explanation thereof is omitted.

Figure 18 shows a first modification of the BLACG circuit shown in Fig. 17(b). This Fig. 18 shows the portion generating the real carry signal C_i. The other portions are omitted.

As shown in Fig. 18, the BLACG (block look ahead carry generator) circuit 105a comprises an AND circuit 1511, a NOR circuit 1512 and an inverter circuit 1513. A first input of the AND circuit 1511 is supplied with a real carry signal c_M'-m' , a second input of the AND circuit 1511 is supplied with a cumulative block carry propagate signal CP_i* and an output of the AND circuit 1511 is connected to a first input of the NOR circuit 1512. A second input of the NOR circuit 1512 is supplied with a cumulative block carry generate signal CG_i*, an output of the NOR circuit 1512 is connected to an input of the inverter circuit 1513, and the inverter circuit 1513 outputs a real carry signal C_i.

This first modification of the third embodiment obtains the real carry signal C_i , according to the above-mentioned equation (19), by inverting by an inverter the output of an AND-OR-inverter which processes the cumulative block carry propagate signal CP_i*, the cumulative block carry generate signal CG_i*, and the real carry signal C_M'-m'.

According to the first modification of the third embodiment, it is possible to construct the circuit with the least number of circuit elements. However, the circuit is somewhat slow in processing speed. Still, the difference is 1 to 2 ns in the case of use of 1 to 1.5 µm CMOS elements and less than 10 percent of the 15 to 20 ns time required for full addition of 64 bits, so does not pose a problem in practice.

Figure 19 shows a second modification of the third embodiment. Figure 19 shows only the important portions in the same way as Fig. 18.

As shown in Fig. 19, the BLACG circuit 105a comprises a NOR circuit 1521, a first and a second inverter circuits 1522 and 1523 and a first and a second transfer gate circuits 1524 and 1525. A first input of the NOR circuit 1521 is supplied with a cumulative block carry propagate signal CP_i*, a second input of the NOR circuit 1521 and an input of the first inverter circuit 1522 are connected and supplied with a cumulative block carry generate signal CG_i*. An output of the NOR circuit 1521 is connected to an input of the first transfer gate circuit 1524 and an output of the first inverter circuit 1522 is connected to an input of the second transfer gate circuit 1525. A first control gate of the first transfer gate circuit 1524 and a second control gate of the second transfer gate circuit 1525 are connected and supplied with a real carry signal C_M'-m', and a second control gate of the first transfer gate circuit 1524 and a first control gate of the second transfer gate circuit 1525 are connected and supplied with an inverted real carry signal <maths id="math0061" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>C</mtext></mrow><mrow><mtext>M'-m'</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0061.tif" /></maths>. Outputs of the first and second transfer gate circuits 1524 and 1525 are commonly connected to an input of the second inverter circuit 1523, and the second inverter circuit 1523 outputs a real carry signal C_i.

This second modification of the third embodiment is constructed in accordance with the following equation (20). That is, equation (19) can be interpreted as follows:<maths id="math0062" num="(20)"><math display="block"><mrow><msub><mrow><mtext>C</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext> = CG</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext>* (when C</mtext></mrow><mrow><mtext>M'-m'</mtext></mrow></msub><mtext> = "0")</mtext><mspace linebreak="newline" /><msub><mrow><mtext> = CG</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext>* + CP</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext>* (when C</mtext></mrow><mrow><mtext>M'-m'</mtext></mrow></msub><mtext> = "1")</mtext></mrow></math><img file="EP0347029B1_D0062.tif" /></maths>

According to the second modification of the third embodiment, the number of circuit elements becomes larger compared with the first modification (Fig. 18), but is still less than in the circuit of Fig. 1 and the circuit is equal to that circuit in terms of the processing speed, so by achieving a higher speed of the CG_i* circuit than in the circuitry of Fig. 1, it is possible to shorten the processing time required for the addition.

Figure 20 shows a third modification of the third embodiment and shows only the portions corresponding to the basic principle.

As shown in Fig. 20, the BLACG circuit 105a comprises an EOR circuit 1531, a first and a second inverter circuits 1532 and 1533 and a first and a second transfer gate circuits 1534 and 1535. A first input of the EOR circuit 1531 is supplied with a cumulative block carry propagate signal CP_i* and an output of the EOR circuit 1531 is connected to an input of the first transfer gate circuit 1534. An input of the first inverter circuit 1532 is supplied with a cumulative block carry generate signal CG_i* and an output of the first inverter circuit 1532 and a second input of the EOR circuit 1531 are commonly connected to an input of the second transfer gate circuit 1535. A first control gate of the first transfer gate circuit 1534 and a second control gate of the second transfer gate circuit 1535 are connected and supplied with a real carry signal C_M'-m', a second control gate of the first transfer gate circuit 1534 and a first control gate of the second transfer gate circuit 1535 are connected and supplied with an inverted real carry signal <maths id="math0063" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>C</mtext></mrow><mrow><mtext>M'-m'</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0063.tif" /></maths>. Outputs of the first and second transfer gate circuits 1534 and 1535 are commonly connected to an input of the second inverter circuit 1533, and the second inverter circuit 1533 outputs a real carry signal C_i.

The third modification of the third embodiment takes note of the fact that in equation (19), the cumulative block carry propagate signal CP_i* and the cumulative block carry generate signal CG_i* never simultaneously become "1" and is constructed in accordance with the following equation (21). That is, equation (19) is given as:<maths id="math0064" num="(21)"><math display="block"><mrow><msub><mrow><mtext>Ci = CG</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext>* (when C</mtext></mrow><mrow><mtext>M'-m'</mtext></mrow></msub><mtext> = "0")</mtext><mspace linebreak="newline" /><msub><mrow><mtext> = CG</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext>* ⊕ CP</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext>* (when C</mtext></mrow><mrow><mtext>M'-m'</mtext></mrow></msub><mtext> = "1")</mtext></mrow></math><img file="EP0347029B1_D0064.tif" /></maths>

According to the third modification of the third embodiment, the number of circuit elements becomes larger compared with the second modification (Fig. 19), but by using EOR circuits which are high in speed and have fewer elements, it is possible to achieve a higher speed and greater simplicity compared with the circuitry of Fig. 1.

Figure 21 shows a fourth modification of the third embodiment and shows only the portions corresponding to the basic principle.

As shown in Fig. 21, the BLACG circuit 105a comprises a NAND circuit 1541 and an ENOR circuit 1542. A first input of the NAND circuit 1541 is supplied with a real carry signal C_M'-m' and a second input of the NAND circuit 1541 is supplied with a cumulative block carry propagate signal CP_i*. An output of the NAND circuit 1541 is connected to a first input of the ENOR circuit 1542 and a second input of the ENOR circuit 1542 is supplied with a cumulative block carry generate signal CG_i*, and the ENOR circuit 1542 outputs a real carry signal C_i.

The fourth modification of the third embodiment modifies equation (19) to the following equation (22) so as to simplify the circuit:<maths id="math0065" num="(22)"><math display="block"><mrow><msub><mrow><mtext>C</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext> = CG</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext>* ⊕ (CP</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext>*·C</mtext></mrow><mrow><mtext>M'-m'</mtext></mrow></msub><mtext>)</mtext></mrow></math><img file="EP0347029B1_D0065.tif" /></maths>

Figure 22 shows a fifth modification of the third embodiment and shows only the portions corresponding to the basic principle.

As shown in Fig. 22, the BLACG circuit 105a comprises a NAND circuit 1551, a first, a second and a third inverter circuits 1552, 1553 and 1554 and a first and a second transfer gate circuits 1555 and 1556. A first input of the NAND circuit 1551 is supplied with a real carry signal C_M'-m' and a second input of the NAND circuit is supplied with a cumulative block carry propagate signal CP_i*, an output of the NAND circuit 1551 is connected to an input of the first inverter circuit 1552 and a second control gate of the first transfer gate circuit 1555 and a first control gate of the second transfer gate circuit 1556. An output of the first inverter circuit 1552 is connected to a first control gate of the first transfer gate circuit 1555 and a second control gate of the second transfer gate circuit 1556. An input of the second inverter circuit 1553 and an input of the first transfer gate circuit 1555 are connected and supplied with a cumulative block carry generate signal CG_i*, an output of the second inverter circuit 1553 is connected to an input of the second transfer gate circuit 1556. Outputs of the first and second transfer gate circuits 1555 and 1556 are commonly connected to an input of the third inverter circuit 1554, and the third inverter circuit 1554 outputs a real carry signal C_i.

The fifth modification of the third embodiment is constructed using a transfer gate TG for the ENOR circuit portion of the fourth modification (Fig. 21). In this way, it is possible to simplify the circuit by using a transfer gate TG.

Figure 23 shows a sixth modification of the third embodiment.

As shown in Fig. 23, the BLACG circuit 105a comprises a first and a second transfer gate circuits 1561 and 1562 and an inverter circuit 1563. An input of the first transfer gate circuit 1561 is supplied with an inverted real carry signal <maths id="math0066" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>C</mtext></mrow><mrow><mtext>M'-m'</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0066.tif" /></maths>, an input of the second transfer gate circuit 1562 is supplied with an inverted cumulative block carry generate signal <maths id="math0067" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>CG</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext>*</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0067.tif" /></maths>. A first control gate of the first transfer gate circuit 1561 and a second control gate of the second transfer gate circuit 1562 are connected and supplied with a cumulative block carry propagate signal CP_i*, a second control gate of the first transfer gate circuit 1561 and a first control gate of the second transfer gate circuit 1562 are connected and supplied with an inverted cumulative block carry propagate signal <maths id="math0068" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext>CP</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext>*</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0068.tif" /></maths>. Outputs of the first and second transfer gate circuits 1561 and 1562 are commonly connected to an input of the inverter circuit 1563, and the inverter circuit 1563 outputs a real carry signal C_i.

This sixth modification of the third embodiment is obtained by considering the fact that in equation (19), the cumulative carry propagate signal CP_i* and the cumulative carry generate signal CG_i* never simultaneously become "1" and making the interpretation that:<maths id="math0069" num="(23)"><math display="block"><mrow><msub><mrow><mtext>C</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext> = CG</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext>* (when CP</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext>* = "0")</mtext><mspace linebreak="newline" /><msub><mrow><mtext> = C</mtext></mrow><mrow><mtext>M'-m'</mtext></mrow></msub><msub><mrow><mtext> (when CP</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext>* = "1")</mtext></mrow></math><img file="EP0347029B1_D0069.tif" /></maths>

By making this construction, it is possible to simplify the circuit and to raise the processing speed.

Figure 24 shows a second example of the BLACG circuit according to the third embodiment. Figure 24(a) is a symbolized view of the BLACG circuit 105b of the present embodiment and Fig. 24(b) is a detailed circuit diagram of the same.

While the BLACG circuits 105a shown in Figs. 17 to 23 were constructed using circuits of combinations of NAND, AND, NOR, EOR and ENOR circuits and inverters as the CP_i* and CG_i* generating circuits, the BLACG circuit 105b according to the second example of the third embodiment replaces these-with chain circuits of the wired OR circuits of transfer gates TG and inverter circuits INV to secure equivalent functions as with the prior BLACG circuits 105a.

As shown in Fig. 24(b), for the cumulative block carry propagate signal CP_i* (equation (17)), the block carry propagate signal BP₃ of the third digit, which is the lowest digit in the BLACG circuit 105b, is given to the input end of the chain circuit of the transfer gate TG and the inverter INV. The transfer gates of the digits (seventh, 11th, and 15th digits) are controlled ON and OFF by the block carry propagate signals BP_i (BP₇ , BP₁₁ , and BP₁₅) of the digits. At the digits where the transfer gates TG are to be OFF, a signal corresponding to "0" is generated and successively conveyed to the higher digits. The conveyed signal is inverted with each stage of the inverters INV it passes through. Therefore, for the generation of the conveyed signal corresponding to "0", use is made of pull-down NMOS elements and pull-up PMOS elements so that a "0" signal is conveyed to the higher digits at digits where the cumulative block carry propagate signal CP_i* is noninverted and a "1" signal is conveyed at digits where it is inverted.

On the other hand, for the cumulative block carry generate signal CG_i* (equation (18)), the same construction is used as in the case of the above-mentioned cumulative carry propagate signal CP_i*. That is, the input to the chain circuit of the transfer gate TG and the inverter INV is the block carry generate signal BG₃ of the third digit, which is the lowest digit in the said BLACG circuit 105b. The transfer gates of the digits are controlled ON and OFF by the block carry propagate signals BP_i , (BP₇ , BP₁₁ and BP₁₅) of the digits. At the digits where the transfer gates TG are to be OFF, a signal corresponding to the block carry generate signal BG_i is generated and successively conveyed to the higher digits.

Note that in Fig. 24(b), an inverter INV is inserted for each stage of the transfer gates TG in the CP_i* generating circuit, but it may be inserted for every two or three stages of the transfer gates TG or combinations of the same.

In the present example of the third embodiment, as the circuit for generating the real carry signal C_i from the cumulative block carry propagate signal CP_i*, the cumulative block carry generate signal CG_i*, and the carry signal C_M'-m' (in the figure, C_-1), use is made of the circuit of the sixth modification (Fig. 23).

By using such a combination, it is possible to secure an equivalent high speed as in the case of use of the circuit of the second modification (Fig. 19) or the third modification (Fig. 20) with less circuit elements than with the use of the circuit of the first example of the third embodiment (Fig. 17).

In the above example of the third embodiment, there are 71 circuit elements, so it is possible to halve the 136 elements of the example of Fig. 1 and thus possible to considerably cut down on the number of circuit elements without sacrificing high speed.

To achieve simultaneously a reduction in the number of circuit elements and a high speed of processing, use may be made of the BLACG circuit 105b of the second example of the third embodiment (Fig. 24) as the BLACG circuit for processing the lower digits and use may be made of a circuit comprised of a combination of a circuit which generates the cumulative block carry propagate signal CP_i* and cumulative block carry generate signal CG_i* by a chain circuit of a transfer gate TG and inverter INV with the second modification (Fig. 19).

Note that the above explanation was made in reference to a number of block bits m = m' = 4, but that in general it is possible that m # m' or that m # 4.

Further, out of the data A and B to be processed, the values of the number of block bits m (or m') may differ between a higher digit and lower digit.

Further, it is possible, instead of the pregeneration of the presumed sum signals F_i(0) and F_i(1) in the lower digit to directly calculate the real sum signal F_i as:<maths id="math0070" num="(24)"><math display="block"><mrow><msub><mrow><mtext>F</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext> = P</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext> ⊕ C</mtext></mrow><mrow><mtext>i-1</mtext></mrow></msub></mrow></math><img file="EP0347029B1_D0070.tif" /></maths> and select and output the presumed sum signals F_i(0) and F_i(1) (or similar signals) by the value of the carry signal of C_M-1 of just the higher digit, by which method it is possible to further simplify the circuit.

Figures 24 to 27 show other examples of the third embodiment. Namely, Fig. 24(a) is a block diagram showing a BLACG circuit 105a in the parallel full adder shown in Fig. 16, and Fig. 24(b) is a circuit diagram showing a second example of the BLACG circuit shown in Fig. 24(a), Fig. 25 is a block diagram showing a second example of application to a 64 bit ALU of a parallel full adder according to the third embodiment of the present invention, Fig. 26(a) is a block diagram showing a BLACG circuit 105c in the parallel full adder shown in Fig. 25, and Fig. 26(b) is a circuit diagram showing a third example of the BLACG circuit shown in Fig. 26(a), and Fig. 27(a) is a block diagram showing a BLACG circuit 105d in the parallel full adder shown in Fig. 25, and Fig. 27(b) is a circuit diagram showing a fourth example of the BLACG circuit shown in Fig. 27(a).

As shown in Figs. 24(b), 26(b) and 27(b), the BLACG circuits 105b, 105c and 105d comprise a chain circuit mutually connected with a transfer gate circuit and an inverter circuit.

In the second example of the third embodiment, the point of difference with the BLACG circuits shown in Figs. 17 to 24 and the example of Figs. 1 to 3 lies in the constitution of the BLACG circuit. The same construction is taken for the input data A, B, the ULB circuit 100, the CSA circuit 101, and the first MPX circuit 102, so the same symbols are appended and explanations thereof are omitted.

The BLACG circuits 105c and 105d of the third and fourth examples according to the third embodiment, when finding the real carry signal C_i by the block carry propagate signal BP_i , the block carry generate signal BG_i , and the carry signal C_M'-m' , does not only engage in one stage of processing by the BLACG circuit 105a as in the first example of application to the 64 bit ALU of the parallel full adder (Fig. 16), but engages in processing divided into two stages (105c, 105d) or more stages.

That is, in the first example of application to the ALU (Fig. 16), four digits' worth of block carry propagate signals BP_i and block carry generate signals BG_i are assembled and the real carry signals C_i of those digits are generated. In the present embodiment, instead of this, regarding the four digits of input signals, the lower three digits' worth of real carry signals and the highest digit's cumulative block carry propagate signal CP_i* and cumulative block carry generate signal CG_i* are generated by the BLACG circuit 105c. The cumulative block carry propagate signal CP_i* and the cumulative block carry generate signal CG_i* output from the BLACG circuits 105c are output to the BLACG circuit 105d. At the BLACG circuit 105d, the carry signal C_in from the digit (i = -1) below the highest digit of n bits and CP_i* and CG_i* are processed in 105d and the real carry signal C_i is generated. The processing here is the same as in the case of the first example of application to the ALU (Fig. 16). The real carry signal C_i generated is input to the BLACG circuit 105c as the carry signal from the lower digit. The carry signal is confirmed as the three digits' worth of real carry signals to be processed in the BLACG circuit 105c.

Note that the above explanation was made with reference to a two-stage construction of the BLACG circuits 105c and 105d. In the case of more stages, it is sufficient to repeat the same type of process as above.

According to the above second and third examples of application to the ALU, the number of circuit elements required slightly increases over that of the first example (Fig. 16), but since the ripple carry processing is replaced by parallel processing, the generation of the real carry signal C_i can be made high speed and it is possible to maintain the high speed with an overall number of circuit elements less than in the prior art.

The above first to fourth examples and first to sixth modifications of the third embodiments show examples of parallel full adders, but the present invention can, in a fourth embodiment,also be applied to parallel fully subtracters (not illustrated).

In the fourth embodiment of a parallel full subtracter, similar to the relationship between the first and second embodiments, the carry propagate signal P_i as spoken of in the case of an adder becomes a "borrow propagate signal" and the carry generate signal G_i becomes a "borrow generate signal". The borrow propagate signal P_i in this case is given by the ENOR of<maths id="math0071" num="(3)'"><math display="block"><mrow><msub><mrow><mtext>P</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext> = </mtext><mover accent="true"><mrow><msub><mrow><mtext>A</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><msub><mrow><mtext> ⊕ B</mtext></mrow><mrow><mtext>i</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0347029B1_D0071.tif" /></maths> Further, the borrow generate signal G_i is given by<maths id="math0072" num="(4)'"><math display="block"><mrow><msub><mrow><mtext>G</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext> = </mtext><mover accent="true"><mrow><msub><mrow><mtext>A</mtext></mrow><mrow><mtext>i</mtext></mrow></msub></mrow><mo>¯</mo></mover><msub><mrow><mtext>·B</mtext></mrow><mrow><mtext>i</mtext></mrow></msub></mrow></math><img file="EP0347029B1_D0072.tif" /></maths> Further, the cumulative block carry propagate signal CP_i* is used as the "cumulative block borrow propagate signal" and the cumulative block carry generate signal CG_i* is used as the "cumulative block borrow generate signal" and, in addition, the carry signal C_M'-m' is used as the "borrow signal C_M'-m'" and the operation is performed successively from the lowest digit to the highest digit. At this time, M is the lowest digit of the signal to be processed in the block subtracter (CSA corresponding circuit 201) to which the i-th digit belongs, and M' is the lowest digit of the signal to be processed in the BLACG corresponding circuit which processes the i-th digit cumulative block borrow propagate signal CP_i* and the cumulative block borrow generate signal CG_i*. With such a signal setting, it is possible to construct a parallel full subtracter using the circuits shown in the above-mentioned first to fourth examples and first to sixth modifications of the third embodiments and obtain the real difference signal F_i, corresponding to an inverted signal of the real sum signal F_i in the adder circuits. Therefore, a detailed explanation will be omitted.

As explained above, an embodiment of the present invention can provide a binary operator using the block select look ahead system which serves as a parallel full adder and parallel full subtracter able to greatly cut down on the number of elements of the circuit without sacrificing the high speed of the computation since two presumed sum signals are never generated in parallel.

As a result, a parallel full adder (or full subtracter) for processing long-bit data, may be relatively easily realised in an LSI circuit in which only a limited number of elements can be accommodated.