This post presents a bunch of **numerical problems on the asynchronous counter (or ripple counter) & synchronous counter**. You will get solutions to the problems as well. Students preparing for B.E./B.Tech semester examinations and GATE will find this post and the numerical problems useful.

**Problem number 1**

**Problem statement:**

Calculate the frequency of a **4-bit ripple counter, **if the period of the** **waveform at the last flip-flop is 64 microseconds.

**Answer:**

In a 4-bit ripple counter, four flip-flops (FF0to FF3) are used. The input frequency of flip-flop FF0 is ‘f ‘and its output waveform frequency is f/2 which is applied as input of FF1. Consequently, the output waveform frequency of FF1 is f/4 which is used as input of FF2. Then output waveform frequency of FF2 is f/8 which is used as input of FF3. Therefore, the output waveform frequency of FF3 is f/16 and the time period is T=1/frequency=16/f.

Since the time period of the last flip-flop (FF3) is 64 microseconds,

T=16/f=64 x 10^{-6,}

Then clock frequency of a 4-bit ripple counter is ‘f’ =16/ (64 x 10^{-6}) Hz=250 kHz.

**Problem number 2**

**Problem statement:**

A 4-bit **asynchronous binary counter** is shown in Figure (a) below. Each D flip-flop is negative edge-triggered and has a propagation delay for 10 nanoseconds (ns). Develop a **timing diagram** showing the *Q *output of each flip-flop, and determine the **total propagation delay time** from the triggering edge of a clock pulse until a corresponding change can occur in the state of *Q*3. Also, determine the **maximum clock frequency **at which the counter can be operated.

**Answer**:

The **timing diagram** with delays omitted is as shown in Figure (b).

For the total delay time, the effect of CLK16 must propagate through four flip-flops before *Q*3 changes,

So the **total propagation delay time,**

*tp*(*tot*) is = 4 * 10 ns = **40 ns****.**

**The maximum clock frequency is,**

*f*max =1/*tp*(*tot*)

=1/40 ns = **25 MHz**

The counter should be operated below this frequency to avoid problems due to the propagation delay.

**Problem number 3**

**Problem statement:**

If the input frequency on the left is 60 Hz, find out the output frequency from the modulo-6 counter. Also, find out the output frequency from the decade counter.

**Solution :**

Here is the diagram from which it is clear that the output frequency from the modulo-6 counter will be 60/6=10 Hz and this is the input clock frequency for the decade counter. So the output frequency from the decade counter is 10/10=1Hz.

Practically decade counter followed by a modulo-6 counter is used as a divide-by-60 circuit and used as a 1-second timer.

**Problem number 4**

**Problem statement:**

(a) Determine *f*_{max} for the synchronous counter of the Figure below, if *t*_{pd} for each FF is 50 ns and *t*_{pd} for each AND gate is 20 ns. Compare this value with *f*_{max} for a MOD-16 ripple counter.

(b) What must be done to convert this counter to MOD-32?

(c) Determine *f*_{max} for the MOD-32 parallel counter.

**Solution**

- (a) In a synchronous counter, the total delay that must be allowed between input clock pulses is equal to FF
*t*_{pd}+ AND gate*t*_{pd}. Thus, the period*T*_{clock}= 50 + 20 = 70 ns, and so the synchronous counter has a maximum frequency of*f*_{max}=1/*T*=1/70 ns = 14.3 MHz

A MOD-16 ripple counter uses four FFs with *t*_{pd} = 50 ns.

From Equation, *T*_{clock }= *N ** *t*_{pd}. Thus, *f*_{max} for the ripple counter is *f*_{max} =1/*T*=1/4 * 50 ns= 5 MHz

- (b) A fifth FF must be added because 2
^{5 }= 32. The*CLK*input of this FF is also tied to the input pulses. Its*J*and*K*inputs are fed by the output of a four-input AND gate whose inputs are*A*,*B*,*C*, and*D.*

- (c)
*f*_{max}is still determined as in (a) regardless of the number of FFs in the parallel counter (synchronous counter). Thus,*f*_{max}is still 14.3 MHz.

## 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 S. Saha*, who is an assistant professor in a renowned degree engineering college in India. Professor Saha teaches subjects related to digital electronics & microprocessors.