Design a two bit down counter circuit that count from 11 to 00. The initial state of the counter may be assumed to be 11. The counter will be in following successive states: 11, 10, 01, 00, 11, 10, 01, 00, 11 … Use any flip flop to design the circuit. You must design them using state transition diagram and Karnaugh’s map.
Course Code : BCSL022
Course Title : Assembly Language Programming Lab
Assignment Number : BCA(II)/L022/Assignment/2015
Maximum Marks : 50
Weightage : 25%
Solution :
A sequential circuit is specified by a time sequence of external inputs, external outputs and internal flipflop binary states. Thus firstly, a state table and state diagram is used to describe behaviour of the circuit.
Present State

Input 
Next State 
FlipFlops Inputs 

A

B 
X 
A

B 
DA 
DB 
0

0 
0 
0 
0 
1 
1 
0

0 
1 
0 
1 
1 
0 
0

1 
0 
0 
1 
1 
0 
0

1 
1 
1 
0 
0 
1 
1 
0 
0

1 
0 
0 
1 
1 
0 
1

1 
1 
0 
0 
1

1 
0 
1 
1 
0 
0 
1

1 
1 
0 
0 
1 
1 
There are 2 flipflop inputs for counter i.e. A, B. The next state of flipflop is given in the table. DA indicates the flip flop input corresponding to flipflopA. This counter requires 2flipflops.
From this the flip flop input equations are simplified using KMaps as shown below.
KMap for DA is:
KMap for DB is:
Thus, the simplified input equations for BCD counter are:
DA = ABC + AB + AC
DB = BC + BC
The logic circuit can be made with 2 D flip flops, 2 OR gates & 4 AND gates.