Visualise half adders, full adders, and ripple-carry adder chains
Binary addition follows column-by-column rules: 0+0=0, 0+1=1, 1+1=10 (sum 0 carry 1). The carry propagates to the next more-significant bit.
Half adder: Sum = A⊕B, Carry = A·B. Cannot accept carry-in — only usable for the LSB. Full adder: three inputs (A, B, Cin); built from two half adders plus OR for carry-out.
Ripple-carry chains n full adders; delay grows linearly with bit width. Carry-lookahead computes carry signals in parallel using generate (G=A·B) and propagate (P=A⊕B) terms, reducing delay to O(log n).