MOD 10 Synchronous Counter using D Flip-flop

This post is about how to design a MOD 10 Synchronous Counter or Decade Counter using D Flip-flop step by step.

MOD 10 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 10. i.e., M = 10

Therefore, 10 ≤ 2^N 

=> N = 4

Therefore, to design a MOD 10 or Decade Counter, 4 flip-flops will 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 10 Synchronous Counter using D Flip-flop will be

QA	QB	QC	QD	QA+1	QB+1	QC+1	QD+1	DA	DB	DC	DD
0	0	0	0	0	0	0	1	0	0	0	1
0	0	0	1	0	0	1	0	0	0	1	0
0	0	1	0	0	0	1	1	0	0	1	1
0	0	1	1	0	1	0	0	0	1	0	0
0	1	0	0	0	1	0	1	0	1	0	1
0	1	0	1	0	1	1	0	0	1	1	0
0	1	1	0	0	1	1	1	0	1	1	1
0	1	1	1	1	0	0	0	1	0	0	0
1	0	0	0	1	0	0	1	1	0	0	1
1	0	0	1	0	0	0	0	0	0	0	0
1	0	1	0	X	X	X	X	X	X	X	X
1	0	1	1	X	X	X	X	X	X	X	X
1	1	0	0	X	X	X	X	X	X	X	X
1	1	0	1	X	X	X	X	X	X	X	X
1	1	1	0	X	X	X	X	X	X	X	X
1	1	1	1	X	X	X	X	X	X	X	X

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 & D_D

K Map for D_A :

Therefore,  D_A = Q_AQ_D^/ + Q_BQ_CQ_D

K Map for D_B  : 

Therefore, D_B = Q_BQ_C^/ + Q_BQ_D^/ + Q_B^/Q_CQ_D

K Map for  D_C:

Therefore, D_C = Q_CQ_D^/ + Q_A^/Q_C^/Q_D

K Map for  D_D :

Therefore, D_D = Q_D^/ 

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

Circuit for MOD 10 or Decade Synchronous Counter using D Flip-flop:

In this way "MOD 10 Synchronous Counter using D Flip-flop" can be designed.

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