Binary Counter — Terminal Count in DOWN Mode (3-Bit) For a 3-bit binary counter operating in DOWN mode, what is the terminal count (the state at which it rolls under to the maximum state)?

Introduction / Context:
Terminal count (TC) denotes the count at which a counter rolls over (or under) and optionally generates a carry/borrow pulse for cascading. For a DOWN counter, the sequence decrements each clock and wraps when it reaches the minimum representable state.

Given Data / Assumptions:

• Width: 3 bits (states 000 through 111).
• DOWN mode: sequence proceeds 111 → 110 → … → 000 → wrap to 111.
• Binary, no gray or BCD coding involved.

Concept / Approach:
In 3-bit binary, the smallest state is 000, and the largest is 111. A DOWN counter decrements until it reaches 000. The next decrement causes wraparound to 111. Therefore, the terminal count for DOWN operation is the minimum state 000 (often the condition that asserts a “borrow” or terminal-count flag).

Step-by-Step Solution:
Enumerate downward: 111, 110, 101, 100, 011, 010, 001, 000.Identify wrap point: after 000, the sequence returns to 111.Thus, terminal count (before wrap) = 000.

Verification / Alternative check:
Examine a simple synchronous 3-bit subtract-one design; comparators flag the 000 state to force reload/borrow and wrap back to 111 on the next tick.

Why Other Options Are Wrong:

• 111: That is the terminal count for UP mode (wrap from max to 000).
• 101, 010: Intermediate states, not wrap points.

Common Pitfalls:
Confusing UP vs DOWN sequences or misinterpreting “terminal count” as any max/min rather than the wrap state specific to the chosen count direction.

Final Answer:
000