BCD Adder (4-bit)

Adds two 4-bit BCD digits (0–9) using two 74HC283 binary adder ICs. Stage 1 performs binary addition; if sum > 9, the K detector triggers Stage 2 to add +6 (0110) as a correction.

4-Bit BCD Adder — 2 × IC 74HC283

GROUP A GROUP B 0 A3 0 A2 0 A1 0 A0 0 B3 0 B2 0 B1 0 B0 A3 A2 A1 A0 B3 B2 B1 B0 74HC283 BINARY ADDER — A + B Stage 1 — Cᵢₙ = 0 S3 S2 S1 S0 C₀ K DETECTOR K = C₁ + S₃S₂ + S₃S₁ if sum > 9 → K = 1 K = 0 S3 S2 S1 S0 74HC283 CORRECTION ADDER B₃=0 B₂=K B₁=K B₀=0 Z3 Z2 Z1 Z0 BCD SUM DIGIT 0 Z3 0 Z2 0 Z1 0 Z0 0 BCD CARRY
A = 0 (0000)
B = 0 (0000)
Sum = 0
✓ Valid — no correction

Why add 6?

Binary 4-bit can represent 0–15, but valid BCD only goes 0–9. Codes 10–15 are illegal in BCD. Adding 6 (0110) skips over those 6 illegal codes, wrapping the result back into a valid BCD digit and propagating a carry to the tens position.

Detection Logic

K = C₁ + S₃·S₂ + S₃·S₁
  • • C₁ = 1: binary sum > 15 (overflow)
  • • S₃·S₂: sum is 12–15 (1100–1111)
  • • S₃·S₁: sum is 10–11 (1010–1011)