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Decimal and Shorter Counts
States Count

To create a decimal counter, we need to find a way to cut the counting sequence short. The Truth Table to the left shows the actual counting sequence we need. Note that the counting sequence is exactly the same as for the binary counter we saw on the previous page, up through a count of 9. At that point, where the binary counter would continue on to a count of 10, the decimal counter must reset itself to a count of 0.

In this sequence, flip-flops A and C are no problem. Their next states will both be logic 0 whether the next count is 10 or 0. However, flip-flop B would normally switch from logic 0 to logic 1, and must be prevented from doing so. At the same time, flip-flop D, which is at logic 1, must be made to switch back to logic 0.

Hmmmm. Since flip-flop D is a logic 1 for only two counts, and only flip-flop A will change state going from count 8 to count 9 in any case, perhaps we can use the D and D' outputs, with gates, to force the desired change in sequence. This is in fact the case, as shown in the demonstration below. Note that we have applied different signals to the J and K inputs of flip-flop D. This is perfectly acceptable, and allows us to reset this flip-flop under the control of a simple two-input AND gate.

0 0 0 0 0
0 0 0 1 1
0 0 1 0 2
0 0 1 1 3
0 1 0 0 4
0 1 0 1 5
0 1 1 0 6
0 1 1 1 7
1 0 0 0 8
1 0 0 1 9

Synchronous decimal counter.

The base-6 counter (counting from 0-5) is just a shorter version of the decimal counter. Flip-flop D is no longer needed, but the logic of controlling the count is not really different. The demonstration to the right shows a practical counter for the 10s of minutes or seconds in a digital clock.

Synchronous base-6 counter.

Now that we've seen counting sequences other than binary, new questions arise: Can we generate other counting sequences for special purposes? And are there other uses for counting circuits than numeric counts? We'll explore these questions on the next page.

Prev: Synchronous Binary Counter Next: Frequency Dividers

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