MOD 8 Synchronous Counter using D Flip-flop

This post is about how to design a MOD-8 Synchronous Counter using D Flip-flop step by step.

MOD 8 Synchronous Counter using D Flip-flop

Step 1: Find the number of Flip-flops needed

The number of Flip-flops  required can be determined by using the following equation:

M ≤ 2^N 

where, M is the MOD number and N is the number of required flip-flops.

Here, MOD number is equal to 8. i.e., M = 8

Therefore, 8 ≤ 2^N 

=> N = 3

Therefore, to design a MOD 8 Counter, 3 flip-flops would be required.

Step 2: Write the excitation table of the flip-flop

Excitation table of D flip-flop is:

QN	QN+1	D
0	0	0
0	1	1
1	0	0
1	1	1

Step 3: Write the circuit state table by using excitation table

Circuit state table for designing MOD 8 Synchronous Counter using D Flip-flop would be

QA	QB	QC	QA+1	QB+1	QC+1	DA	DB	DC
0	0	0	0	0	1	0	0	1
0	0	1	0	1	0	0	1	0
0	1	0	0	1	1	0	1	1
0	1	1	1	0	0	1	0	0
1	0	0	1	0	1	1	0	1
1	0	1	1	1	0	1	1	0
1	1	0	1	1	1	1	1	1
1	1	1	0	0	0	0	0	0

Step 4: Prepare K Map for each flip-flop input in terms of flip-flop outputs as the input variables

In this case inputs of the flip-flops are:  D_A, D_B & D_C 

K Map for D_A :

Therefore,  D_A = Q_A^/Q_BQ_C + Q_AQ_B^/ + Q_AQ_C^/

K Map for D_B :

Therefore, D_B = Q_B XOR Q_C

K Map for  D_C:

Therefore, D_C =  Q_C^/

Step 5: Draw the circuit using flip-flops and other gates correspond to the minimized expressions

Circuit for MOD 8 Synchronous Counter using D Flip-flop would be

In this way "MOD 8 Synchronous Counter using D Flip-flop" can be designed.

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