Prerequisite – Counters
Problem – Design synchronous counter for sequence: 0 → 1 → 3 → 4 → 5 → 7 → 0, using T flip-flop.
Explanation – For given sequence, state transition diagram as following below:
State transition table logic:
Present State | Next State |
---|---|
0 | 1 |
1 | 3 |
3 | 4 |
4 | 5 |
5 | 7 |
7 | 0 |
State transition table for given sequence:
Present State | Next State | ||||
---|---|---|---|---|---|
Q_{3} | Q_{2} | Q_{1} | Q_{3}(t+1) | Q_{2}(t+1) | Q_{1}(t+1) |
0 | 0 | 0 | 0 | 0 | 1 |
0 | 0 | 1 | 0 | 1 | 1 |
0 | 1 | 1 | 1 | 0 | 0 |
1 | 0 | 0 | 1 | 0 | 1 |
1 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 0 | 0 |
T flip-flop – If value of Q changes either from 0 to 1 or from 1 to 0 then input for T flip-flop is 1 else input value is 0.
Qt | Qt+1 | T |
---|---|---|
0 | 0 | 0 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 0 |
Draw input table of all T flip-flops by using the excitation table of T flip-flop. As nature of T flip-flop is toggle in nature. Here, Q3 as Most significant bit and Q1 as least significant bit.
Input table of Flip-Flops | |||
---|---|---|---|
T_{3} | T_{2} | T_{1} | |
0 | 0 | 1 | |
0 | 1 | 1 | |
1 | 1 | 0 | |
0 | 0 | 0 | |
0 | 1 | 0 | |
1 | 1 | 1 |
Find value of T_{3}, T_{2}, T_{1} in terms of Q_{3}, Q_{2}, Q_{1} using K-Map (Karnaugh Map):
Therefore,
T_{3} = Q_{2}
Therefore,
T_{2} = Q_{1} + Q_{2}
Therefore,
T_{1} = Q_{3}’Q_{2}’ + Q_{3}Q_{2}
Now, you can design required circuit using expressions of K-maps:
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