- Synchronous counter is designed to count the number of clock pulses.
- This counter is clocked with the same clock signal and at the same time.
- Synchronous counters can be formed using T or JK flip flops and are edge triggered.
- The flip flops will change their present state only when the next clock pulse arrives.

## Design Steps:

The basic design steps for these counters are discussed in detail.

- First we find the number of flip flops required for the design of a synchronous counter.
- The number of flip flops can be determined from 2^n ≥ N.

Where: N →number of states and n →number of flip flops.

- Next ew select the flip flop for the design.
- Then we draw the state diagram of that counter.
- With the help of an excitation table of flip flops we determine the excitation table of the counter.
- At last we simplify the excitation table using K-map.

## Design for Mod-N counter

The design of the mod-N synchronous counter is done through following steps.

**Step 1 :** **Find number of flip flops **

For the mod N counter we can find the number of flip flops from relation

**N <= 2n**

Let us consider N= 10. So,

**For n =3, **10<=8, which is not true. Hence again considering n= 4

** **10<=16

This holds true.

Therefore the number of flip flops required is 4 for the Mod-10 counter.

**Step 2 : Excitation table of Flip flops **

We chose a T flip flop for the design. Then the excitation table for T flip flop is as shown

**Step 3 : State diagram andCircuit excitation table **

The mod-10 counter counts ten states from 0 to 9. This counter is also called the decade counter. We use four flip flops here. They are reset When QD QC QB QA = 1001.

**Circuit excitation table **

Now QD QC QB QA are the present states of flip-flops and Q*D Q*C Q*B Q*A is the next counting state of these Flip flops.

When there is transition in the present of QD the value changes from 0 to 1 or vice versa.

**Step 4 : Simplify K-map for each FF input in terms of flip-flop outputs as the input variable **

**Step 5 :Circuit diagram **

The negative edge trigger is used for toggle.

- The clock pulse is synchronous to all flip flops.
- Then the input to every flip flop is as per the equation of K map.