# 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

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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 1
1 1 0
0 0 0
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 + Q2`

Therefore,

`T1 = Q3’Q2’ + Q3Q2 `

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