GATE CS 2011 Q15 — Sequential Circuits

A modulo-$N$ (or mod-$N$) counter goes through $N$ unique states. To represent these $N$ states, we need $n$ flip-flops such that the total number of possible states, $2^n$, is at least $N$.

The relationship is given by the inequality:

Given $N = 258$:

Let's evaluate for different values of $n$:

• For $n = 8$: $2^8 = 256 < 258$ (insufficient to represent $258$ states)
• For $n = 9$: $2^9 = 512 \ge 258$ (sufficient)

Thus, the minimum number of $\text{D}$ flip-flops required is 9.