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# Digital Circuits

## Number System and Base Conversion

The numbers we are familiar with and use every day are based on 10 symbols and rules for making and displaying all numbers, both positive and negative, from them. This system of numbers is the decimal system.  Note that in the decimal system the base is 10; we have 10 …

## Variable Sampling

In the processes or machinery that are controlled by a microcontroller or microprocessor, all analog data must be converted to digital, so that it can be represented by binary numbers and be usable by the microprocessor. When a variable entity such as wind speed, car speed, or electric current in …

## One’s and Two’s Complement of Binary Number

For the analysis of practical applications, it is necessary to do mathematical operations on binary numbers. This is the basis of all that a microprocessor does. In this section, we study how two binary numbers are added, how one is subtracted from the other. We also discuss how the negative …

## Karnaugh Map Tutorial with Solved Examples | K-Map

An alternative to the truth table to determine and simplify the logic function for an application is Karnaugh map (K-Map), named after its originator Karnaugh. Karnaugh map abbreviates to K-map offers a simpler solution to find the logic function for applications with two, three, and four inputs. Its application to …

## Boolean Algebra Laws with Examples

The Boolean algebra is a set of specific rules that governs the mathematical relationships corresponding to the logic gates and their combinations. Their application is limited to two-valued (0 and 1) entries such as the inputs and outputs of logic gates. Dealing with one single gate and a pair of …

## Multiplexer and Demultiplexer

Multiplexer and demultiplexer are two devices very important in data communications. As the name implies, their functions are opposite to each other (similar to encoder and decoder). These devices are used for sharing a device between two or more applications. Consider, for instance, a decoder for seven-segment display. If we …

## Encoder and Decoder

Data can be stored in the form of binary numbers. Depending on the number of digits available, the magnitude of information stored changes, but more information can always be stored with less data. Having 4 bits of storage (say, four flip-flops), for example, offers the possibility of 24 = 16 …

## Flip-Flop in Digital Electronics

A flip-flop is the basic memory element for storing a bit of information. It is an edge-triggered device. That is, it reacts to the edge of a pulse. A simple flip-flop has two stable states (remember, for instance, that a capacitor has two states: charged and discharged). States are represented …

## Basic Logic Gates | Definition | Truth Tables | Examples

Electronic switching circuits that govern, or “decide,” whether inputs will pass to output or be stopped are called logic gates. The logic gates discussed here are the building blocks for other logic gates. The basic logic gates are: AND gates. OR gates. NOT gates. NAND gates. NOR gates. XOR gates. …

## Binary Number System Basics

Definition: Digital electronic circuits can be made to act in only two states: on and off. This two-state system is called a binary number system. This system can be compared to a single-pole, single-throw (SPST) switch, Figure 1. A switch in the off position represents a 0 in the binary …

## Latches and Flip Flops

The goal of this module is to explore Sequential Logic and its functional building blocks and to describe the operations of latches and flip-flops in digital circuits. Objective A learner will be able to: Explain the difference between combinatorial logic and sequential logic. Define positive and negative edge triggering. Explain …

## Logic Simplification Karnaugh map

The goal of this module is to provide learners with tools for reducing Boolean algebra expressions to their simplest form. Objectives The learner will be able to: Reduce Boolean expressions using the 14 Boolean rules. Simplify complex Boolean algebra expressions using the 14 Boolean rules and apply DeMorgan’s Theorem. Carry …

## Combinational Logic Circuits using Logic Gates

The goal of this module is to provide learners with tools for understanding the operations of XNOR and XOR gates and enable learners to apply Boolean rules to find the Sum of Products (SOP) and the Product of Sums (POS). Objectives The learner will be able to: Explain the operation …