Let's design a synchronous BCD counter. A BCD counter follows a sequence of ten states and returns to 0 after count of 9. These counters are also known as decade counters. This type of counter is useful in display applications in which BCD is essential for conversion to a decimal readout. Figure demonstrates characteristic table for this counter.

Figure: Characteristic table for decade counter

There are 4 flip-flop inputs for Decade counter it implies A, B, C, D.  The subsequent state of flip-flop is given in table. J_A and K_A denotes flip flop input corresponding to flip-flop-A.  Please note this counter need 4-flip-flops.

From this flip flop input equations are simplified by K-Maps as displayed in figure below.  Unused minterms from 1010 through 1111 are considered as don't care conditions.

Figure:  K-maps for Decade counter

So simplified input equation for BCD counter are as below:

Logic circuit can be designed with 4 JK flip flops and 3 AND gates.

Figure: Logic Diagram for decade counter.