Design counter for given sequence

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
Q3	Q2	Q1	Q3(t+1)	Q2(t+1)	Q1(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
T3	T2	T1
0	0	1
0	1	0
1	1	1
0	0	1
0	1	0
1	1	1

Find value of T₃, T₂, T₁ in terms of Q₃, Q₂, Q₁ using K-Map (Karnaugh Map): Therefore,

T3 = Q2 

Therefore,

T2 = Q1 

Therefore,

T1 = Q2+Q1'

Now, you can design required circuit using expressions of K-maps: