Question

designe a counter that follow 113022601

Answer 1

I have solved in a clear manner, Please don't forget to upvote

Solution:

To design a counter that follows the sequence 1 - 1 - 3 - 0 - 2 - 2 - 6 - 0 - 1.

Since the question didn't specify synchronous or Asynchronous,

I consider Synchronous counter.

Step 1:

Construct the state transition diagram

Step 2:

By using the state transition diagram we can build the state transition table logic:

The total number of states is 9.

Present State	Next State
1	1
1	3
3	0
0	2
2	2
2	6
6	0
0	1
1	1

Step 3:

Construction of State Transition Table by using the state transition table logic

The maximum number in the sequence is 6,

We need a minimum of 3 binary bit to represent number 6,

So, lets us consider the state assignment as 3 binary for each number,

We can get the state transition table as follows:

Present State			Next State
Q3	Q2	Q1	Q3(t+1)	Q2(t+1)	Q1(t+1)
0	0	1	0	0	1
0	0	1	0	1	1
0	1	1	0	0	0
0	0	0	0	1	0
0	1	0	0	1	0
0	1	0	1	1	0
1	1	0	0	0	0
0	0	0	0	0	1
0	0	1	0	0	1

Step4:

To design the sequence using flipflops

Let us consider the D-flipflop

the excitation table of the D-flipflop is given below:

Present state	Next State	D-Flip flop input(D)
0	0	0
0	1	1
1	0	0
1	1	1

We can observe that the input of the D-flipflop is equal to the next state;

Step5:

Construction of Circuit Excitation Table, we get

Step6:

Solving for the D flipflop inputs with respect to the present state, we get as

For D_A by considering Q₃, Q₂, Q₁,

we get as

Q3\Q2Q1	00	01	11	10
0		1
1

we get D_A = Q₃' Q₂Q₁

For D_B by considering Q₃, Q₂, Q₁,

we get as

Q3\Q2Q1	00	01	11	10
0	1	1		1
1

we get D_B = Q₃'Q₁' + Q₃'Q₂'

For D_C by considering Q₃, Q₂, Q₁,

we get as

Q3\Q2Q1	00	01	11	10
0	1	1
1

we get D_C = Q₃'Q₂'

Step 7:

By using the equation for the input of the D flip flop. let us construct the circuit,

we get the circuit as follows