Modulo-16 ripple counter — state after multiple clocks A MOD-16 (4-bit) ripple up-counter currently shows 1001₂ (decimal 9). After applying 31 additional clock pulses, what binary count will appear at its outputs?

Introduction / Context:
A MOD-16 binary counter cycles through 16 distinct states (0–15) and then repeats. When asked for the state after many clock pulses, the key is to apply modular arithmetic rather than simulating every intermediate count. This is a staple technique for quickly determining counter outputs in design and troubleshooting.

Given Data / Assumptions:

• The counter is a 4-bit ripple up-counter (natural binary sequence).
• Present state = 1001₂ = 9₁₀.
• Additional pulses = 31.
• Modulus = 16, so states wrap every 16 counts.

Concept / Approach:
Use modulo arithmetic: NewState = (Current + Pulses) mod 16. This yields the equivalent number of steps within a single 0–15 cycle. Convert the final decimal result back to binary for the required output format.

Step-by-Step Solution:

Verification / Alternative check:
Split 31 into 16 + 15. Advancing 16 steps leaves the counter unchanged (modulus property). From 9, advance 15 steps: 9 → 24, then wrap 24 − 16 = 8, which is 1000₂. Same result, confirming the calculation.

Why Other Options Are Wrong:

• 1010₂ (10), 1011₂ (11), 1101₂ (13), 0111₂ (7): none equals 8, so they do not match the modulo arithmetic outcome.

Common Pitfalls:

• Forgetting to apply modulo reduction and attempting to count linearly, which is time-consuming and error-prone.
• Misconverting between decimal and binary (e.g., confusing 1000₂ with 8 vs. 1001₂ with 9).

Final Answer:
1000₂