### MOD 10 Synchronous Counter using T Flip-flop

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

## MOD 10 Synchronous Counter using T 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 T flip-flop is:

 QN QN+1 T 0 0 0 0 1 1 1 0 1 1 1 0

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

Circuit state table for designing MOD 10 Synchronous Counter using T 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:  TA, TB, TC & TD

K Map for TA :

Therefore,  TA = QAQD + QBQCQD

K Map for TB  :

Therefore, TB =  QCQD

K Map for  TC:

Therefore, TC =  QA/QD

K Map for  TD :

Therefore, TD  = 1

### 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 T Flip-flop:

In this way "MOD 10 Synchronous Counter using T Flip-flopcan be designed.