# Logic diagram, operation, & timing diagram of a 2-bit Synchronous Binary Counter using J-K flip-flops

In this post, we will cover the Logic diagram, operation, & timing diagram of a 2-bit Synchronous Binary Counter using J-K flip-flops. In one of the earlier posts, we have discussed How to design a Synchronous counter in a step-by-step guide.

## Logic diagram of a2-bit synchronous binary counter

Figure 1(a) shows a 2-bit synchronous binary counter. Notice that an arrangement different from that for the asynchronous counter must be used for the J1 and K1 inputs of FF1 in order to achieve a binary sequence.

## Operation of a 2-bit synchronous binary counter using J-K flip-flop

The operation of a J-K flip-flop synchronous counter is as follows: First, assume that the counter is initially in the binary 0 state; that is, both flip-flops are RESET.

When the positive edge of the first clock pulse is applied, FF0 will toggle and Q0 will therefore go HIGH.

What happens to FF1 at the positive-going edge of CLK1? To find out, let’s look at the input conditions of FF1. Inputs J1 and K1 are both LOW because Q0, to which they are connected, has not yet gone HIGH.

Remember, there is a propagation delay from the triggering edge of the clock pulse until the Q output actually makes a transition.

So, J = 0 and K = 0 when the leading edge of the first clock pulse is applied. This is a no-change condition, and therefore FF1 does not change state. A timing detail of this portion of the counter operation is shown in Figure7(b).

## Summary

Since it goes through a binary sequence, the counter in Figure 1(a) is a binary counter. It actually counts the number of clock pulses up to three (22-1=3), and on the fourth pulse, it recycles to its original state (Q0 = 0, Q1=0).

The term recycle is commonly applied to counter operation; it refers to the transition of the counter from its final state back to its original state.

## Related posts (for further study) on Binary Counter

Asynchronous Counter – study & revision notes

Synchronous Counter – Study & Revision Notes

How to design a Synchronous counter – step by step guide

2-bit Synchronous Binary Counter using J-K flip-flops

A 3-Bit Asynchronous Binary Counter – Up Counter

Asynchronous Up counter for Positive & Negative edge-triggered flip-flops

Binary Counter Sequential Circuit – FAQs

Frequently Asked Questions on Flip-Flops Sequential Circuit

Numerical problems on asynchronous counter & synchronous counter

J-K flip-flop – Frequently asked questions for semester & GATE exam

Modulus-M (MOD-M) asynchronous counter – Study and revision notes

Digital Electronics – Hub page

Author of this post

This post is co-authored by Professor Saraswati Saha, who is an assistant professor at RCCIIT, a renowned degree engineering college in India. Professor Saha teaches subjects related to digital electronics & microprocessors.

Logic diagram, operation, & timing diagram of a 2-bit Synchronous Binary Counter using J-K flip-flops
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