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австралийский геккон (Diplodactylus)
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сумматор последовательного дейстия
сумматор последовательный
[ɪm,pɪərɪəl'stəun]
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имперский, английский или британский стон или стоун
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In computing, the Kogge–Stone adder (KSA or KS) is a parallel prefix form carry look-ahead adder. Other parallel prefix adders (PPA) include the Sklansky adder (SA), Brent–Kung adder (BKA), the Han–Carlson adder (HCA), the fastest known variation, the Lynch–Swartzlander spanning tree adder (STA), Knowles adder (KNA) and Beaumont-Smith adder (BSA).
The Kogge–Stone adder takes more area to implement than the Brent–Kung adder, but has a lower fan-out at each stage, which increases performance for typical CMOS process nodes. However, wiring congestion is often a problem for Kogge–Stone adders. The Lynch–Swartzlander design is smaller, has lower fan-out, and does not suffer from wiring congestion; however to be used the process node must support Manchester carry chain implementations. The general problem of optimizing parallel prefix adders is identical to the variable block size, multi level, carry-skip adder optimization problem, a solution of which is found in Thomas Lynch's thesis of 1996.
An example of a 4-bit Kogge–Stone adder is shown in the diagram. Each vertical stage produces a "propagate" and a "generate" bit, as shown. The culminating generate bits (the carries) are produced in the last stage (vertically), and these bits are XOR'd with the initial propagate after the input (the red boxes) to produce the sum bits. E.g., the first (least-significant) sum bit is calculated by XORing the propagate in the farthest-right red box (a "1") with the carry-in (a "0"), producing a "1". The second bit is calculated by XORing the propagate in second box from the right (a "0") with C0 (a "0"), producing a "0".
4-bit Kogge-Stone adder, Radix-2, without Cin:
'Step 0 P00 = A0 XOR B0 '1dt, S0, dt - type delay time G00 = A0 AND B0 '1dt, C0 P10 = A1 XOR B1 '1dt G10 = A1 AND B1 '1dt P20 = A2 XOR B2 '1dt G20 = A2 AND B2 '1dt P30 = A3 XOR B3 '1dt G30 = A3 AND B3 '1dt 'Step 1, Distance=Radix^(Step-1)=2^0=1, valency-2 G11 = G10 OR P10 AND G00 '3dt, C1 P21 = P20 AND P10 '2dt G21 = G20 OR P20 AND G10 '3dt P31 = P30 AND P20 '2dt G31 = G30 OR P30 AND G20 '3dt 'Step 2, Distance=Radix^(Step-1)=2^1=2, valency-2 G22 = G21 OR P21 AND G00 '4dt, C2 G32 = G31 OR P31 AND G11 '5dt, C3 'Sum S1 = P10 XOR G00 '2dt S2 = P20 XOR G11 '4dt S3 = P30 XOR G22 '5dt
4-bit PPA valency-2,3,4 adder (is 4-bit CLA valency-2,3,4 adder and 4-bit Sklansky valency-2,3,4 adder and 4-bit Kogge-Stone valency-2,3,4 adder and 4-bit Beaumont-Smith valency-2,3,4 adder):
P00 = A0 XOR B0 '1dt, S0 G00 = A0 AND B0 '1dt, C0 P10 = A1 XOR B1 '1dt G10 = A1 AND B1 '1dt P20 = A2 XOR B2 '1dt G20 = A2 AND B2 '1dt P30 = A3 XOR B3 '1dt G30 = A3 AND B3 '1dt G11 = G10 OR_ P10 AND G00 '3dt, C1, valency-2, distance-1 G21 = G20 OR_ P20 AND G10 OR_ P20 AND P10 AND G00 '3dt, C2, valency-3, distance-1,2 G31 = G30 OR_ P30 AND G20 OR_ P30 AND P20 AND G10 OR_ P30 AND P20 AND P10 AND G00 '3dt, C3, valency-4, distance-1,2,3 S0 = P00 '1dt S1 = P10 XOR G00 '2dt S2 = P20 XOR G11 '4dt S3 = P30 XOR G21 '4dt
4-bit Kogge-Stone adder, Radix-2, with Cin:
G0a = A0 AND Cin '1dt G0b = B0 AND Cin '1dt G0c = A0 AND B0 '1dt P00 = A0 XOR B0 '1dt G00 = G0a OR G0b OR G0c '2dt, C0 P10 = A1 XOR B1 '1dt G10 = A1 AND B1 '1dt P20 = A2 XOR B2 '1dt G20 = A2 AND B2 '1dt P30 = A3 XOR B3 '1dt G30 = A3 AND B3 '1dt G11 = G10 OR P10 AND G00 '4dt, C1 P21 = P20 AND P10 '2dt G21 = G20 OR P20 AND G10 '3dt P31 = P30 AND P20 '2dt G31 = G30 OR P30 AND G20 '3dt G22 = G21 OR P21 AND G00 '5dt, C2 G32 = G31 OR P31 AND G11 '6dt, C3, Cout S0 = P00 XOR Cin '2dt S1 = P10 XOR G00 '3dt S2 = P20 XOR G11 '5dt S3 = P30 XOR G22 '6dt
8-bit Kogge-Stone adder, valency-2, radix-4:
P00 = A0 XOR B0 '1dt, S0 G00 = A0 AND B0 '1dt, C0 P10 = A1 XOR B1 '1dt G10 = A1 AND B1 '1dt P20 = A2 XOR B2 '1dt G20 = A2 AND B2 '1dt P30 = A3 XOR B3 '1dt G30 = A3 AND B3 '1dt P40 = A4 XOR B4 '1dt G40 = A4 AND B4 '1dt P50 = A5 XOR B5 '1dt G50 = A5 AND B5 '1dt P60 = A6 XOR B6 '1dt G60 = A6 AND B6 '1dt P70 = A7 XOR B7 '1dt G70 = A7 AND B7 '1dt G11 = G10 OR P10 AND G00 '3dt, C1 P21 = P20 AND P10 '2dt G21 = G20 OR P20 AND G10 '3dt P31 = P30 AND P20 '2dt G31 = G30 OR P30 AND G20 '3dt P41 = P40 AND P30 '2dt G41 = G40 OR P40 AND G30 '3dt P51 = P50 AND P40 '2dt G51 = G50 OR P50 AND G40 '3dt P61 = P60 AND P50 '2dt G61 = G60 OR P60 AND G50 '3dt P71 = P70 AND P60 '2dt G71 = G70 OR P70 AND G60 '3dt G22 = G21 OR P21 AND G00 '5dt, C2 G32 = G31 OR P31 AND G11 '5dt, C3 P42 = P41 AND P21 '4dt G42 = G41 OR P41 AND G21 '5dt P52 = P51 AND P31 '4dt G52 = G51 OR P51 AND G31 '5dt P62 = P61 AND P41 '4dt G62 = G61 OR P61 AND G41 '5dt P72 = P71 AND P51 '4dt G72 = G71 OR P71 AND G51 '5dt G43 = G42 OR P42 AND G00 '7dt, C4 G53 = G52 OR P52 AND G11 '7dt, C5 G63 = G62 OR P62 AND G22 '7dt, C6 G73 = G72 OR P72 AND G32 '7dt, C7, Cout S0 = P00 '1dt S1 = P10 XOR G00 '2dt S2 = P20 XOR G11 '4dt S3 = P30 XOR G22 '6dt S4 = P40 XOR G32 '6dt S5 = P50 XOR G43 '8dt S6 = P60 XOR G53 '8dt S7 = P70 XOR G63 '8dt
8-bit Kogge-Stone adder, valency-2,3,4, radix-4:
P00 = A0 XOR B0 '1dt, S0 G00 = A0 AND B0 '1dt, C0 P10 = A1 XOR B1 '1dt G10 = A1 AND B1 '1dt P20 = A2 XOR B2 '1dt G20 = A2 AND B2 '1dt P30 = A3 XOR B3 '1dt G30 = A3 AND B3 '1dt P40 = A4 XOR B4 '1dt G40 = A4 AND B4 '1dt P50 = A5 XOR B5 '1dt G50 = A5 AND B5 '1dt P60 = A6 XOR B6 '1dt G60 = A6 AND B6 '1dt P70 = A7 XOR B7 '1dt G70 = A7 AND B7 '1dt G11 = G10 OR P10 AND G00 '3dt, C1, valency-2, distance=4^0=1 G21 = G20 OR_ P20 AND G10 OR_ P20 AND P10 AND G00 '3dt, C2, valency-3, distance-1,2 G31 = G30 OR_ P30 AND G20 OR_ P30 AND P20 AND G10 OR_ P30 AND P20 AND P10 AND G00 '3dt, C3, valency-4, distance-1,2,3 P41 = P40 AND P30 AND P20 AND P10 '2dt, valency-4, distance-1,2,3 G41 = G40 OR_ P40 AND G30 OR_ P40 AND P30 AND G20 OR_ P40 AND P30 AND P20 AND G10 '3dt, valency-4, distance-1,2,3 P51 = P50 AND P40 AND P30 AND P20 '2dt, valency-4, distance-1,2,3 G51 = G50 OR_ P50 AND G40 OR_ P50 AND P40 AND G30 OR_ P50 AND P40 AND P30 AND G20 '3dt, valency-4, distance-1,2,3 P61 = P60 AND P50 AND P40 AND P30 '2dt, valency-4, distance-1,2,3 G61 = G60 OR_ P60 AND G50 OR_ P60 AND P50 AND G40 OR_ P60 AND P50 AND P40 AND G30 '3dt, valency-4, distance-1,2,3 P71 = P70 AND P60 AND P50 AND P40 '2dt, valency-4, distance-1,2,3 G71 = G70 OR_ P70 AND G60 OR_ P70 AND P60 AND G50 OR_ P70 AND P60 AND P50 AND G40 '3dt, valency-4, distance-1,2,3 'valency=2, distance=4^1=4 G42 = G41 OR P41 AND G00 '5dt, C4 G52 = G51 OR P51 AND G11 '5dt, C5 G62 = G61 OR P61 AND G21 '5dt, C6 G72 = G71 OR P71 AND G31 '5dt, C7 S0 = P00 '1dt S1 = P10 XOR G00 '2dt S2 = P20 XOR G11 '4dt S3 = P30 XOR G21 '4dt S4 = P40 XOR G31 '6dt S5 = P50 XOR G42 '6dt S6 = P60 XOR G52 '6dt S7 = P70 XOR G62 '6dt
8-bit PPA valency-2,3,4,5,6,7,8 adder (is 8-bit CLA valency-2,3,4,5,6,7,8 adder and 8-bit Sklansky valency-2,3,4,5,6,7,8 adder and 8-bit Kogge-Stone valency-2,3,4,5,6,7,8 adder):
P00 = A0 XOR B0 '1dt, S0 G00 = A0 AND B0 '1dt, C0 P10 = A1 XOR B1 '1dt G10 = A1 AND B1 '1dt P20 = A2 XOR B2 '1dt G20 = A2 AND B2 '1dt P30 = A3 XOR B3 '1dt G30 = A3 AND B3 '1dt P40 = A4 XOR B4 '1dt G40 = A4 AND B4 '1dt P50 = A5 XOR B5 '1dt G50 = A5 AND B5 '1dt P60 = A6 XOR B6 '1dt G60 = A6 AND B6 '1dt P70 = A7 XOR B7 '1dt G70 = A7 AND B7 '1dt '------------------------------------------ G11 = G10 OR P10 AND G00 '3dt, C1, valency-2, distance-1 G21 = G20 OR_ '3dt, C2, valency-3, distance-1,2 P20 AND G10 OR_ P20 AND P10 AND G00 G31 = G30 OR_ '3dt, C3, valency-4, distance-1,2,3 P30 AND G20 OR_ P30 AND P20 AND G10 OR_ P30 AND P20 AND P10 AND G00 G41 = G40 OR_ '3dt, C4, valency-5, distance-1,2,3,4 P40 AND G30 OR_ P40 AND P30 AND G20 OR_ P40 AND P30 AND P20 AND G10 OR_ P40 AND P30 AND P20 AND P10 AND G00 G51 = G50 OR_ '3dt, C5, valency-6, distance-1,2,3,4,5 P50 AND G40 OR_ P50 AND P40 AND G30 OR_ P50 AND P40 AND P30 AND G20 OR_ P50 AND P40 AND P30 AND P20 AND G10 OR_ P50 AND P40 AND P30 AND P20 AND P10 AND G00 G61 = G60 OR_ '3dt, C6, valency-7, distance-1,2,3,4,5,6 P60 AND G50 OR_ P60 AND P50 AND G40 OR_ P60 AND P50 AND P40 AND G30 OR_ P60 AND P50 AND P40 AND P30 AND G20 OR_ P60 AND P50 AND P40 AND P30 AND P20 AND G10 OR_ P60 AND P50 AND P40 AND P30 AND P20 AND P10 AND G00 G71 = G70 OR_ '3dt, C7, valency-8, distance-1,2,3,4,5,6,7 P70 AND G60 OR_ P70 AND P60 AND G50 OR_ P70 AND P60 AND P50 AND G40 OR_ P70 AND P60 AND P50 AND P40 AND G30 OR_ P70 AND P60 AND P50 AND P40 AND P30 AND G20 OR_ P70 AND P60 AND P50 AND P40 AND P30 AND P20 AND G10 OR_ P70 AND P60 AND P50 AND P40 AND P30 AND P20 AND P10 AND G00 '-------------------------------------- S0 = P00 '1dt S1 = P10 XOR G00 '2dt S2 = P20 XOR G11 '4dt S3 = P30 XOR G21 '4dt S4 = P40 XOR G31 '4dt S5 = P50 XOR G41 '4dt S6 = P60 XOR G51 '4dt S7 = P70 XOR G61 '4dt
8-bit PPA valency-2,3,4,5,6,7,8 adder:
P00 = A0 XOR B0 '1dt, S0 G00 = A0 AND B0 '1dt, C0 P10 = A1 XOR B1 '1dt G10 = A1 AND B1 '1dt P20 = A2 XOR B2 '1dt G20 = A2 AND B2 '1dt P30 = A3 XOR B3 '1dt G30 = A3 AND B3 '1dt P40 = A4 XOR B4 '1dt G40 = A4 AND B4 '1dt P50 = A5 XOR B5 '1dt G50 = A5 AND B5 '1dt P60 = A6 XOR B6 '1dt G60 = A6 AND B6 '1dt P70 = A7 XOR B7 '1dt G70 = A7 AND B7 '1dt S1 = P10 XOR G00 S2 = P20 XOR G10 OR P10 AND G00 '4dt, valency-2, distance-1 S3 = P30 XOR G20 OR_ '4dt, valency-3, distance-1,2 P20 AND G10 OR_ P20 AND P10 AND G00 S4 = P40 XOR G30 OR_ '4dt, valency-4, distance-1,2,3 P30 AND G20 OR_ P30 AND P20 AND G10 OR_ P30 AND P20 AND P10 AND G00 S5 = P50 XOR G40 OR_ '4dt, valency-5, distance-1,2,3,4 P40 AND G30 OR_ P40 AND P30 AND G20 OR_ P40 AND P30 AND P20 AND G10 OR_ P40 AND P30 AND P20 AND P10 AND G00 S6 = P60 XOR G50 OR_ '4dt, valency-6, distance-1,2,3,4,5 P50 AND G40 OR_ P50 AND P40 AND G30 OR_ P50 AND P40 AND P30 AND G20 OR_ P50 AND P40 AND P30 AND P20 AND G10 OR_ P50 AND P40 AND P30 AND P20 AND P10 AND G00 S7 = P70 XOR G60 OR_ '4dt, valency-7, distance-1,2,3,4,5,6 P60 AND G50 OR_ P60 AND P50 AND G40 OR_ P60 AND P50 AND P40 AND G30 OR_ P60 AND P50 AND P40 AND P30 AND G20 OR_ P60 AND P50 AND P40 AND P30 AND P20 AND G10 OR_ P60 AND P50 AND P40 AND P30 AND P20 AND P10 AND G00 G71 = G70 OR_ '3dt, C7, valency-8, distance-1,2,3,4,5,6,7 P70 AND G60 OR_ P70 AND P60 AND G50 OR_ P70 AND P60 AND P50 AND G40 OR_ P70 AND P60 AND P50 AND P40 AND G30 OR_ P70 AND P60 AND P50 AND P40 AND P30 AND G20 OR_ P70 AND P60 AND P50 AND P40 AND P30 AND P20 AND G10 OR_ P70 AND P60 AND P50 AND P40 AND P30 AND P20 AND P10 AND G00
The Kogge-Stone adder concept was developed by Peter M. Kogge and Harold S. Stone, who published it in a seminal 1973 paper titled A Parallel Algorithm for the Efficient Solution of a General Class of Recurrence Equations.