Step 1: Understanding the Concept:
A MOD-$N$ counter is a digital circuit that cycles through $N$ unique states.
A counter built with $n$ flip-flops can have a maximum of $2^n$ distinct states.
Step 2: Key Formula or Approach:
To find the required number of flip-flops ($n$), we use the inequality:
\[ 2^n \geq N \]
where $n$ must be the smallest integer satisfying the condition.
Step 3: Detailed Explanation:
For a MOD-16 counter, $N = 16$.
We test values of $n$:
If $n = 3$, $2^3 = 8$ (Too small, as $8<16$).
If $n = 4$, $2^4 = 16$ (Exact match, as $16 \geq 16$).
Thus, 4 flip-flops are needed to represent binary states from $0000$ to $1111$ (0 to 15).
Step 4: Final Answer:
4 flip-flops are required to build a MOD-16 counter.