Up/Down Counters — Next State in DOWN Mode A 4-bit up/down binary counter is operating in the DOWN mode and currently in state 1100 (decimal 12). What state will it go to on the next active clock pulse?

Introduction / Context:
Binary counters are ubiquitous in timing and sequencing. Correctly predicting the next state of an up/down counter reinforces understanding of binary arithmetic and counter direction control. Here, we analyze the DOWN mode behavior from a given 4-bit state.

Given Data / Assumptions:

• Counter width: 4 bits (Q3 Q2 Q1 Q0).
• Present state: 1100 (binary) = 12 (decimal).
• Counter direction: DOWN (decrement by 1 each count).
• No terminal count reload or modulus less than 16 is implied.

Concept / Approach:
In DOWN mode, the next state equals current state minus one, computed in binary with borrow as needed. For a straight 4-bit binary counter without truncation, the sequence near 12 goes: 1100 → 1011 → 1010 ... down to 0000, then wraps to 1111 on the subsequent count.

Step-by-Step Solution:
Interpret 1100 as decimal 12.Compute 12 − 1 = 11.Convert 11 to binary: 1011.Therefore, next state is 1011.

Verification / Alternative check:
Subtract one in binary directly: 1100 − 0001 → borrow from Q2 into Q1 Q0 yields 1011, confirming the arithmetic.

Why Other Options Are Wrong:

• 1101: That is +1 (UP mode), not −1.
• 1111: That is the wrap state after 0000 in DOWN counting, not immediately after 1100.
• 0000: Many counts away (12 steps) from 1100 in DOWN mode.

Common Pitfalls:
Adding instead of subtracting, or assuming immediate wrap without reaching 0000 first.

Final Answer:
1011