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Fast Carry Generation

Carry Look Ahead Adder - Truth Table, Boolean Expression & CMOS Circuit | Logicroo

Learn the Carry Look Ahead Adder with interactive circuit diagrams, truth tables, Boolean expressions, carry generation and propagation, CMOS implementation, timing diagrams, and digital logic examples.

Carry Look-Ahead Adder

Fast Carry Generation

Instead of waiting for each stage's carry to ripple in, every bit position first computes a Generate (Gi = Ai·Bi) and Propagate (Pi = Ai⊕Bi) signal. A single two-level AND–OR network then expands those into every carry bit at once — so total delay stays roughly constant as the adder grows wider, instead of scaling with N like a ripple-carry chain.

A (3→0)
B (3→0)
Cin
Sum
0000
Cout
0
A (dec)
0
B (dec)
0
Sum (dec)
0
Delay
Gi = Ai · Bi  ·  Pi = Ai ⊕ Bi (1 gate delay, all bits in parallel)
Ci+1 = Gi + PiGi-1 + PiPi-1Gi-2 + ⋯ + Pi⋯P0C0 (2-level AND-OR, all carries in parallel)  ·  Sumi = Pi ⊕ Ci
No stage waits on a neighbor's output  ·  worst-case total delay ≈ , independent of N (vs 2N = 8Δ for a 4-bit ripple-carry adder)
Sample truth table (Cin = 0)
ABSumCout