Down counter

Also called: count-down counter, decrementing counter, binary down counter

A counter that subtracts 1 at each active clock edge, stepping 111, 110, … , 000 and then wrapping back to all 1s.

A down counter runs a binary counter backwards. Each edge subtracts 1, and from all 0s it wraps to all 1s: 000 → 111 → 110 → …

Subtracting 1 flips the trailing 0s to 1 and the lowest 1 to 0. So the toggle rule turns around:

A bit toggles exactly when every bit below it is 0 (that is when a borrow reaches it).
Q0 has nothing below it, so it still toggles every edge.

That gives the hardware directly:

Synchronous, with T flip-flops: T0 = 1, T1 = , T2 = , T3 = .
Ripple, with positive-edge flip-flops: clock each stage from the previous Q (not ). Q rises exactly when the bit below goes 0 → 1, which is when a borrow passes through it.

A down counter's terminal count is the all-0s state, the last one before it wraps. Down counters are popular for timers: load a value, count to zero, and raise a flag.

Worked examples

Example

One edge from 100

A 3-bit synchronous down counter of T flip-flops holds Q2Q1Q0 = 100 (4).

1.
T0 = 1 → Q0 toggles 0 → 1.
2.
T1 = = 1 (Q0 was 0) → Q1 toggles 0 → 1.
3.
T2 = = 1·1 = 1 → Q2 toggles 1 → 0.
4.
New count 011 = 3 = 4 − 1 ✓.

Example

Counting past zero

A 3-bit down counter starts at 010 (2). What does it hold after 5 edges?

1.
2 − 5 = −3.
2.
Wrap into 0…7 by adding 8: −3 + 8 = 5.
3.
So 101. Check by listing: 2 → 1 → 0 → 7 → 6 → 5 ✓.

Common mistakes

Using the up counter's rule. Going down, a bit toggles when every lower bit is 0, not 1.
Wrapping the wrong way. Below 000 comes 111, not 001.
Wiring a positive-edge ripple down counter from . That's the up-counter wiring; a down counter takes each clock from Q.

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