MASTER OF COMPUTER APPLICATIONS
Course Code : MCS012
Course Title : Computer Organisation and Assembly Language Programming
Assignment Number : MCA(I)/012/Assignment/1516
Maximum Marks : 100
Weightage : 25%
Design a two bit counter (a sequential circuit) that counts from 00 to 10 only. Thus, the counter states are 00, 01, 10, 00, 01,…. You should show the state table, state diagram, the kmap for circuit design and logic diagram of the resultant design using D flipflop or JK flip flop.
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 
0 
0 
0

0 
1 
0 
1 
0 
1 
0

1 
0 
0 
1 
0 
1 
0

1 
1 
1 
0 
1 
0 
1 
0 
0

1 
0 
1 
0 
1 
0 
1

1 
1 
0 
0 
1

1 
0 
1 
1 
0 
0 
1

1 
1 
0 
0 
0 
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 Counter are:
DA = ABX + ABX
DB = ABX + ABX + ABX
The logic circuit can be made with 2 D flip flops, 2 OR gates & 4 AND gates.