The Decade Counter

The Modulo-16 ripple counter can be modified with additional logic gates to provide a base 10 decade counter for use in standard decimal counting and arithmetic.

A decade counter requires resetting to 0 when the count reaches decimal 10. In the case of the ripple counter this corresponds to triggering a CLEAR signal to all 4 flip-flops when the state 1010_bin is reached.

It is therefore necessary to take action when all of the following are true

• Q_a = 0
• Q_b = 1
• Q_c = 0
• Q_d = 1

In principle this would require the logical AND of the outputs Q_b and Q_d and the complements of Q_a and Q_c. In practise however, from the mod-16 counter truth table it can be seen that decimal 10 corresponds to the first time that Q_b and Q_d are 1 and so the logic is simplified.

 

The subsequent circuit for a decade counter is illustrated below where some of the labelling has been omitted for clarity. The additional logic that has been added compared to the modulo-16 ripple counter is indicated in red.

 

When the count reaches 1010_bin then Q_b = Q_d = 1 and so the output from the NAND gate changes from 1 to 0. In this case CLEAR goes from 1 to 0 and causes all of the Q outputs to be reset to 0. At the same time the NOT gate provides a binary 1 to indicate the CARRY condition out of the counter. Once Q_b = Q_d = 0 then the output of the NAND gate returns to 1 and the count can restart.