# Design a decade counter using D-flipflop. Show all the steps involved 10m Dec2005

By | November 8, 2014

Design a decade counter using D-flipflop. Show all the steps involved 10m Dec2005

A BCD counter follows a sequence of ten states and returns to 0 after the count of 9. These counters are also called decade counters. This type of counter is useful in display applications in which BCD is required for conversion to a decimal readout.

 Present State Next State Flip-Flops Inputs A B C D A B C D DA DB DC DD 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0

There are 4 flip-flop inputs for decade counter i.e. A, B, C, D. The next state of flip-flop is given in the table. JA & KA indicates the flip flop input corresponding to flip-flop-A. This counter requires 4-flip-flops.

From this the flip flop input equations are simplified using K-Maps as shown below. The unused minterms from 1010 through 1111 are taken as don’t care conditions (X).

K-Map for Da is:

K-Map for Db is:

K-Map for Dc is:

K-Map for Dd is:

Thus, the simplified input equations for BCD counter are:

Da = BCD + A|D

Db = |BCD + B|C + B|D

Dc = |A|CD + C|D

Dd = |D

The logic circuit can be made with 4 D flip flops, 3 OR gates & 7 AND gates