### 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

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 = 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

### 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:  DA, DB, DC & DD

K Map for DA :

Therefore,  DA = QAQD/ + QBQCQD

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