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Cascaded Full Adders

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

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

Ripple Carry Adder

Cascaded Full Adders

Four full adders chained so the Carry-out of stage i feeds the Carry-in of stage i+1. Each stage can't finish until the previous stage's carry arrives — that propagation delay "rippling" down the chain is what gives this adder its name.

A (3→0)
B (3→0)
Cin
Sum
0000
Cout
0
A (dec)
0
B (dec)
0
Sum (dec)
0
Delay
Stage i: Sumi = Ai ⊕ Bi ⊕ Ci (XOR)  ·  Ci+1 = (Ai · Bi) + (Ci · (Ai ⊕ Bi)) (OR + AND)
Stage i cannot resolve Sumi/Ci+1 until Ci arrives from stage i−1  ·  worst-case total delay ≈ 2N gate delays (2 × 4 = here)
Sample truth table (Cin = 0)
ABSumCout