Skip to content
BetterDL

BCD (decade) counter

Also called: BCD counter, decade counter, mod-10 counter, decimal counter

A mod-10 counter that counts 0000 to 1001 (0 to 9 in BCD) and then returns to 0000, giving one decimal digit per 4-bit stage.

A BCD counter, or decade counter, is a mod n counter with N = 10. It counts in binary-coded decimal: 0000, 0001, … , 1001 (0 to 9), then back to 0000.

  • It needs 4 flip-flops, because 2³ = 8 is too few for 10 states.
  • The six codes 1010 to 1111 are unused states. When designing the next-state logic you can treat them as don't-cares.
  • Its terminal count is 1 at 1001.

Why bother with decimal? Each 4-bit stage holds exactly one decimal digit, which can drive a 7-segment display through a decoder without any binary-to-decimal conversion. Cascade decades by feeding each stage's TC into the next stage's enable: two decades count 00 to 99, three count 000 to 999. Event counters, frequency meters and digital clocks all work this way.

startCLKCLKCLKCLKCLKCLKCLKCLKCLKCLK0000000100100011010001010110011110001001

Worked examples

Example

Two cascaded decades: 39 → 40

A tens decade and a units decade share the clock. The units TC (1 at 1001, with E) drives the tens enable. The display shows 39: tens 0011, units 1001.

  1. 1.

    Units at 1001 with E = 1, so units TC = 1.

  2. 2.

    Tens enabled: 0011 → 0100 (3 → 4).

  3. 3.

    Units wrap: 1001 → 0000.

  4. 4.

    Display: 40 ✓. In plain binary the units would have gone to 1010 instead.

Example

Where does it end up?

A single BCD counter starts at 0110 (6). What does it show after 27 edges?

  1. 1.

    6 + 27 = 33.

  2. 2.

    Mod 10: 33 mod 10 = 3.

  3. 3.

    So 0011. It wrapped through 0 three times along the way.

Common mistakes

  • Letting it count to 1010 or 1111. A BCD counter returns to 0000 straight after 1001.

  • Expecting fewer flip-flops. Ten states still need 4 flip-flops; six codes go unused.

  • Placing the TC at 1111. A decade's last state is 1001.

Practice BCD (decade) counter

Interactive questions with instant feedback and a worked solution for every wrong answer.

Counters lesson full course

Practice exams

Related terms

Learn it step by step

BCD (decade) counter is taught in Counters.

Counters →

All terms