# 3 bit Synchronous Down Counter

• Difficulty Level : Medium
• Last Updated : 19 May, 2021

Prerequisite : Counter , Synchronous counter.

3 bit Synchronous Down Counter :

• In synchronous counter clock is provided to all the flip-flops simultaneously.
• Circuit becomes complex as the number of states increases.
• Speed is high.

Design : The steps involves in design are

1. Decide the number of Flip flops –

N number of Flip flop(FF) required for N bit counter.
• For 3 bit counter we require 3 FF.
• Maximum count = 2n-1, where n is a number of bits.
• For n= 3, Maximum count = 7.
• Here T FF is used.

2. Write excitation table of FF –

3. Draw State diagram and circuit excitation table –
Number of states = 2n, where n is number of bits.

Here T = 1, then there is output state(next state changes from previous state) changes i.e Q changes from 0 to 1 or 1 to 0
T= 0 then, there is no state output state changes i.e Q remains same

4. Find simplified equation using k map –

K map for 3 bit synchronous down counter

5.  Create circuit diagram –
The clock is provided to every Flip flop at same instant of time.
The toggle(T) input is provided to every Flip flop according to the simplified equation of K map.

Timing diagram of 3 bit synchronous Down counter.

Explanation :
Here -ve edge triggered clock is used for toggling purpose.

As we see from characteristics table when T = 1, then toggling takes place and T =0 then it stores the output state.

• Initially Q3 = 0, Q2= 0, Q1= 0.
• In simplified equation of K map we get T1 = 1, therefore Flip flop 1 output Q1 is toggle for every negative edge(because clock is negative edge triggered). Flip-flop(FF) 2 toggle input(T2) is connected to Q’1. Therefore, Flip Flop 2 output state Q2 is toggle only when there is clock falling edge  (i.e -ve edge triggering) and Q’1 =1.
• Similarly, Flip flop 3 toggle input(T) is connected to Q’2 and Q’1. Therefore, Flip flop 3 output is toggle when there is clock falling edge and Q’2=1 and Q’1 = 1 .(as you can see from timing diagram)
• Therefore, we get output(as down counting Q3(MSB) Q2 Q1(LSB) after 8th -ve edge triggered clock the output of the three Flip flops again becomes Q3 = 0, Q2 = 0, Q1 =0.
• We get output(state changes) after every -ve edge clock pulse.
• By 3 Flip flop we get output as 23-1= 7 to 0.
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