# Digital Electronics _21

## Synchronous counter design for irregular sequence

In this post, we will design a Synchronous counter for an irregular sequence using J-K flip-flops with step-by-step analysis. Design a Synchronous counter for an irregular sequence Problem statement: Design a Synchronous counter to generate the following sequence 0->2->5->4->7->0 using J-K flip-flops. Design Solution using J-K flip-flops Step1: State diagram for the given sequence 0->2->5->4->7->0 […]

## Lockout condition in Counter with design to avoid it

In this post, we will discuss the Lockout condition and how to avoid it. We will also design a sequence generator to avoid lockout conditions. What is Lockout Condition in a counter? In a synchronous counter or sequence generator, if the counter or sequence generator finds itself in some unused state, the next state is […]

## Drawing the output waveform for the OR gate & a given pulsed input waveforms

Problem statement: Draw the output waveform for the OR gate and the given pulsed input waveforms of Fig. 1 (a). SolutionFigure 1(b) shows the output waveform. It can be drawn by following the truth table of the OR gate.

## Four-input OR gate using two-input OR gates – How?

How would you hardware-implement a four-input OR gate using two-input OR gates only? SolutionFigure 1 shows one possible arrangement of two-input OR gates that simulates a four-input OR gate. A, B, C and D are logic inputs and Y3 is the output. Figure 2 shows another possible arrangement. In the case of Fig. 1, the […]

## OR Gate – definition, symbol, & Truth table

An OR gate performs an ORing operation on two or more than two logic variables. The OR operation on two independent logic variables A and B is written as Y = A+B and reads as Y equals A OR B and not as A plus B. An OR gate is a logic circuit with two […]

## Truth Table of a logic system

A truth table lists all possible combinations of input binary variables and the corresponding outputs of a logic system. The logic system output can be found from the logic expression, often referred to as the Boolean expression, that relates the output with the inputs of that very logic system. When the number of input binary […]

## Positive and Negative Logic in digital systems

The binary variables can have either of the two states, i.e. the logic ‘0’ state or the logic ‘1’ state. These logic states in digital systems such as computers, for instance, are represented by two different voltage levels or two different current levels. Positive and negative logic systems come into picture here. Positive and Negative […]

## Exclusive-NOR

Two special logic circuits that occur quite often in digital systems are the exclusive-OR and exclusive-NOR circuits. In this post, we will talk about Exclusive-NOR. [ Read about Exclusive-OR here ] Exclusive-NOR The circuit that produces a HiGH output whenever the two inputs are at the same level is called the Exclusive-NOR. The exclusive-NOR circuit […]

## Exclusive-OR

Two special logic circuits that occur quite often in digital systems are the exclusive-OR and exclusive-NOR circuits. In this post, we will talk about Exclusive-OR. [ Read about exclusive-NOR here] Exclusive-OR The circuit that produces a HiGH output whenever the two inputs are at opposite levels is called the Exclusive-OR.This is the exclusive-OR circuit, which […]

## DeMorgan’s theorems of Boolean algebra

Two of the most important theorems of Boolean algebra were contributed by a great mathematician named DeMorgan. DeMorgan’s theorems are extremely useful in simplifying expressions in which a product or sum of variables is inverted. The two theorems are represented as shown in figure 1 below: Statements of DeMorgan’s theorems Theorem (1) of DeMorgan says […]

## Boolean algebra theorems | boolean theorems (rules)

Boolean algebra can be used to help analyze a logic circuit and express its operation mathematically. We will study Boolean algebra by investigating the various boolean theorems (rules) that can help us to simplify logic expressions and logic circuits. Boolean theorems (rules of Boolean algebra) The first group of theorems is given in Figure 1. […]

## Binary System & Binary counting

It is very easy to design simple, accurate electronic circuits that operate with only two voltage levels. For this reason, almost every digital system uses the binary (base-2) number system as the basic number system of its operations. Other number systems (like the decimal system) are often used to interpret or represent binary quantities for […]

## Decimal System with examples

In this post, we will cover Decimal System with examples. The decimal system is composed of 10 numerals or symbols. These 10 symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; using these symbols as digits of a number, we can express any quantity. Decimal System or base-10 system with examples The […]

## Boolean function implementation using multiplexer

Boolean function implementation using multiplexer – In this post, we will solve a numerical problem based on Multiplexers. We also see how to implement the Boolean function using Multiplexers. Here, we have used 8:1 MUX.

## Design steps of 4-bit asynchronous up counter using J-K flip-flop

In this post, we will discuss the Design steps of the 4-bit asynchronous up counter using J-K flip-flops. In a binary counter, if flip-flops do not change states in exact synchronism with the applied clock pulses then the counter is called asynchronous binary counter. In this counter, each FF output drives the CLK input of […]

## Design steps of 4-bit (MOD-16) synchronous up counter using J-K flip-flop

In this post, we will discuss the Design steps of the 4-bit (MOD-16) synchronous up counter using the J-K flip-flop. We will start off by answering a few related questions first. What is synchronous counter? In a synchronous counter, the clock input terminals of all flip-flops are commonly connected. Therefore, the same clock pulse simultaneously […]

## Latch, Flip-flop, and Counter

This post covers Latch, Flip-flop, and Counter with a set of questions and answers. These three topics are very important for digital electronics students. What is the difference between combinational and sequential circuits? Digital logic circuits are classified into two groups. Combinational logic circuits and sequential logic circuits. Combinational logic circuits are circuits in which […]

## Flip-flop Types, Logic symbols, Truth Table & Applications – study notes

The basic building block for sequential logic circuits is the flip-flop. Logic circuits are classified into two groups. One is combination logic circuits using AND, OR, and NOT gates. The other group of circuits is classified as sequential logic circuits. Sequential circuits involve timing and memory devices. The basic building block for sequential logic circuits […]

## Clocked S-R flip-flop & Clocked D Flip-Flop

In this post, we will study the Clocked S-R flip-flop & Clocked D Flip-Flop. S-R flip-flop is also called R-S flip-flop. We have used both the terms here. Clocked S-R flip-flop The RS flip flop is considered one of the most basic sequential logic circuits. The flip-flop is a one bit bistable memory device. It […]

## MOD-6 (Modulus-6) ripple counter – study & revision notes

In this post, we present a detailed write-up on MOD-6 (Modulus-6) ripple counter (study & revision notes). We know that n-bit asynchronous counters can count N = 2n clock pulses, Where n = Number of Flip Flops. For example, a 3-bit counter has 8 different states (0 to 7) and it is a MOD-8 counter. […]

## Propagation Delay in Ripple Counters: Study notes & Numerical problem

In this post, we will study the Propagation Delay in Ripple Counters. We will also solve a sample Numerical problem to illustrate the effect of propagation delays in a 4-bit asynchronous binary counter. Propagation Delay in Ripple Counters – explained Ripple counters are the simplest type of binary counters because they require the fewest components […]

## Asynchronous inputs of the flip-flop – Preset & Clear

In this post, we will know about Asynchronous inputs (or Preset & Clear inputs) of the flip-flop sequential circuit. Asynchronous input versus Synchronous input of flip-flop For the clocked flip-flops, the S, R, J, K, D, and T inputs are normally referred to as control inputs. These are also called synchronous inputs because their effect […]

## Race Around Condition in J-K Flip-Flop

In this post on J-K Flip-Flop, we will study the Race Around Condition in a clocked (level-triggered) JK flip-flop. But before that, we will study the Logic symbol, truth table, operation of Positive-edge triggered J-K flip-flop and the J-K Excitation Table or J-K Transition Table. Finally, we will know about 7476 TTL IC (a J-K […]

## Asynchronous modulus counter

This post covers the Asynchronous modulus counter with the help of a set of frequently asked questions (FAQs) and answers. What does it mean by the term modulus of a counter? The modulus of a counter is the number of unique states through which the counter will sequence. The maximum possible number of states (maximum […]

## Asynchronous Decade Counters, method of partial decoding & glitch

In this post, we will discuss Asynchronous Decade Counters. To start with we will briefly see what an asynchronous counter is and then we will find what a decade counter is. In a binary counter, if flip-flops do not change states in exact synchronism with the applied clock pulses then the counter is called asynchronous […]

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

In this post, we will discuss the modulus-M (MOD-M) asynchronous counter and its design procedure. What is a modulus-M (MOD-M) counter? A modulus-M counter is a counter where M represents the number of states present in the counter. Here M <= 2n , where ‘n’ represents the number of flip-flops required to design the modulus-M […]

## J-K flip-flop – operation, truth table, excitation table

In this post, we cover J-K flip-flop and its operation, truth table, excitation table. This post will help students to prepare for the semester & GATE examination. Explain the operation of the J-K flip-flop with its truth table. This basic operation of a positive edge-triggered J-K flip-flop is illustrated in Figure 1.2 and the logic […]

## Numerical problems on asynchronous counter & synchronous counter

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 […]

## Flip-Flop Sequential Circuit

This post covers Flip-Flop Sequential Circuit in detail with the help of a set of questions on the fundamentals of Flip-flop. Also, find answers to these. We hope, the Students who are interested to learn digital electronics and preparing for exams like GATE will find this post useful. Flip-Flop Sequential Circuit Here is a set […]

## Binary Counter Sequential Circuit

Here, we will study Binary Counter Sequential Circuit with the help of a set of questions and answers. We hope that students who are interested to learn digital electronics and preparing for exams like GATE will find this post useful. Binary Counter Sequential Circuit Here are the questions on the Binary counter sequential circuit with […]

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

In this post, we will discuss the following topics: (a) Asynchronous Up counter for Positive edge-triggered flip-flops & (b) Asynchronous Up counter for Negative edge-triggered flip-flops. For both of these, we will refer to the Logic diagram, Timing diagram, and operational details of the counter. Asynchronous Up counter for Positive edge-triggered flip-flops In this section, […]

## A 3-Bit Asynchronous Binary Counter in UP counting mode | Up Counter

In this post, we will discuss A 3-Bit Asynchronous Binary Counter in UP counting mode. An asynchronous counter is one in which the flip-flops (FF) within the counter do not change states at exactly the same time because they do not have a common clock pulse. In the next section, we will find what exactly […]

## 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 a 2-bit synchronous binary counter Figure 1(a) shows a 2-bit synchronous […]

## How to design a Synchronous counter – step by step guide

In this topic, we will now go through a step-by-step procedure to design a complete synchronous counter. Although we will do it for a specific counting sequence (for example 00-01-10-11), the same steps can be followed for any desired sequence. This detailed guide will help the students to follow every minute step to design a […]

## Synchronous Counter – Study & Revision Notes

Synchronous Counter definition & its benefits over Asynchronous Counter, differences in circuit, Problems found with asynchronous counter,

## Asynchronous Counter – study & revision notes

This post presents a detailed study & revision notes on Asynchronous Counter or ripple counter, design of a 2-Bit Asynchronous Binary Counter with its Logic diagram, operation diagram & timing diagram. In the Asynchronous Counter, the F/Fs are not clocked simultaneously. The output of the previous F/F becomes the clock input for the next F/F. […]

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