4-Bit Carry Lookahead Logic
High-performance arithmetic logic units cannot wait for carry signals to ripple sequentially through multiple bit stages. The carry lookahead logic predicts carry bits in parallel by determining if a bit position independently generates or propagates a carry.
Construct the expanded carry expressions C1, C2, C3, and C4 for a 4-bit block. First, derive the generate (Gi) and propagate (Pi) signals for each bit position i:
Gi = Ai AND Bi Pi = Ai XOR Bi
Then, compute the carry out for each stage directly from these signals and the initial carry Cin. Expand the terms completely so that no carry output depends on a previous carry output:
C1 = G0 OR (P0 AND Cin) C2 = G1 OR (P1 AND G0) OR (P1 AND P0 AND Cin) C3 = G2 OR (P2 AND G1) OR (P2 AND P1 AND G0) OR (P2 AND P1 AND P0 AND Cin) C4 = G3 OR (P3 AND G2) OR (P3 AND P2 AND G1) OR (P3 AND P2 AND P1 AND G0) OR (P3 AND P2 AND P1 AND P0 AND Cin)
Constraints
- Implement strictly combinational logic.
- Do not route
C1,C2, orC3into the logic computing the higher-order carries. - Build all carry expressions simultaneously using only the
A,B, andCininputs.
Topics
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