ISRO CS 2025 Q.53: solution and answer

Official answer: CSource: ISRO's final answer key of 15 May 2026

1. A MOD-16 counter has $16$ states, $0000$ to $1111$, and after $1111$ it wraps to $0000$. A ripple counter built from J-K flip-flops with $J=K=1$ toggles on each clock edge and counts up, one state per clock pulse.

2. The current state is $1001_2=1\cdot 8+0\cdot 4+0\cdot 2+1\cdot 1=9_{10}$.

3. The count returns to $0000$ only after passing $1111$ and wrapping, so the number of pulses is $16-9=7$.

4. Check by counting: $9\to 10\to 11\to 12\to 13\to 14\to 15\to 0$ is $7$ pulses.

5. Other pulse counts do not work: $8$ pulses end at $(9+8)\mathrm{mod}16=1$ ($0001$), $6$ pulses end at $15$ ($1111$), and $5$ pulses end at $14$ ($1110$). Only $7$ pulses give $0000$.