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# Binary Sum Circuit

IP.com Disclosure Number: IPCOM000090837D
Original Publication Date: 1969-Jul-01
Included in the Prior Art Database: 2005-Mar-05
Document File: 1 page(s) / 11K

IBM

## Related People

Weinberger, A: AUTHOR

## Abstract

The binary sum for two digits is ordinarily generated by taking the Exclusive-Or of the half-sum of the digits and the carry into that bit position. As the negative carry-in may not be available or may be inconvenient to develop and the negative carry-out is readily available, this adder utilizes the negative carry-out with the propagate or general functions to obtain the sum according to the Boolean expression S = (H . Cin) + (P . Cout) or S = (H + Cin) . (G + Cout), where H is the half-sum of the digits D and B, P is the Or of A and B, and C is the And of A and B.

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Binary Sum Circuit

The binary sum for two digits is ordinarily generated by taking the Exclusive- Or of the half-sum of the digits and the carry into that bit position. As the negative carry-in may not be available or may be inconvenient to develop and the negative carry-out is readily available, this adder utilizes the negative carry-out with the propagate or general functions to obtain the sum according to the Boolean expression S = (H . Cin) + (P . Cout) or S = (H + Cin) . (G + Cout), where H is the half-sum of the digits D and B, P is the Or of A and B, and C is the And of A and B.

In implementing this Boolean expression in an adder group of three bits A1B1, A2B2, and A3B3, the half-sum H3 is provided in positive and negative form from the third bit position. The carry-in from the preceding group CGin and the carry-out to the next group of bit positions CGout are readily available from the usual look-ahead circuitry. The sum from the third bit position of the group is expressed in the Boolean expression S3 = H3A2B2 + H3(A2+B2) A1B1 + H3 (A2+B2) (A1+B1) CGin + (A3+B3) CGout = H3 G2 + H3P2G1 + H3P2P1 CGin + P3 CGout.

This expression Csan be rewritten as S3 = (H3+P2) (H3+G2+P1) (H3+G1+G1+CGin) (G3 = CGout).

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