- Design a two bit counter circuit that counts from 0 to 2. It should have states 00, 01 and 10.
The initial state of the counter may be assumed to be 00. The counter will be in following
successive states: 00, 01, 10, 00, 01, 10, 00, 01, 10, 00 ... Use J-K flip flop to design the
circuit. You must design the circuit using state transition diagram and Karnaugh's maps.
Answers
Answer:
Solution :
A sequential circuit is specified by a time sequence of external inputs, external outputs and internal flip-flop binary states. Thus firstly, a state table and state diagram is used to describe behaviour of the circuit.
Decade_Counter_D_Flip_Flop_Table_02
Thus, the simplified input equations for Counter are:
DA = |ABX + A|B|X
DB = |A|BX + |AB|X + ABX
Down_Counter_D_Flip_Flop_02
The logic circuit can be made with 2 D flip flops, 2 OR gates & 4 AND gates.
Present State
Input
Next State
Flip-Flops 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 flip-flop inputs for counter i.e. A, B. The next state of flip-flop is given in the table. DA indicates the flip flop input corresponding to flip-flop-A. This counter requires 2-flip-flops.
From this the flip flop input equations are simplified using K-Maps as shown below.
Explanation:
