QB_PH_SEC8_005: Digital Electronics

How many flip-flops are minimally required to construct a synchronous MOD-12 counter?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Counter Modulus Definition**: A MOD-$N$ counter cycles through $N$ distinct states ($0$ through $N-1$). 2. **Flip-Flop Capacity**: Each flip-flop stores 1 binary bit. A cascade of $n$ flip-flops has $2^n$ unique binary states. 3. **Inequality Constraint**: $2^n \ge N$ For $N = 12$: - $n = 3 \implies 2^3 = 8 < 12$ (Insufficient) - $n = 4 \implies 2^4 = 16 \ge 12$ (Sufficient) 4. **Conclusion**: Minimum of 4 flip-flops. Option (B) is correct.