Found 1011 Articles for Digital Electronics

Let's start this tutorial with some basics of SOP form and NOR gates before getting into the details of how to realize a logic function or Boolean expression in SOP form using NOR gates only. SOP Form SOP form stands for Sum of Products form. SOP form is one in which a Boolean expression is expressed as a sum of product terms. For example, $$\mathrm{\mathit{f}\lgroup A, B, C\rgroup=AB+ABC+B\overline{C}}$$ This is a Boolean function expressed in SOP (Sum of Products) form. NOR Gate NOR Gate is a universal logic gate, i.e., NOR gate can be used for realization of any ... Read More

SOP Form SOP form stands for Sum of Products form. SOP form is one in which a Boolean expression is expressed as a sum of product terms. For example, $$\mathrm{\mathit{f}\lgroup A, B, C\rgroup=AB+ABC+B\overline{C}}$$ This is a Boolean function expressed in SOP (Sum of Products) form. NAND Gate The NAND Gate is a type of universal logic gate. It is a logic gate one that can be used to realize any kind of logical function or any other type of logic gate. A NAND gate is basically a combination of two basic logic gates namely AND gate and NOT gate, i.e. ... Read More

In positional number systems, the radix is the total number of unique digits that are used to represent numbers in that number system. Radix is also called Base. For example, in decimal number system, we use total ten digits from 0 to 9 (i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9) to represent any decimal number. Therefore, for the decimal number system, the radix or base is ten (10). Although we can easily convert a given number from one radix (i.e. number system) to any other radix (number system) by using radix conversion protocols. In this article, ... Read More

The K-Map or Karnaugh Map is a systematic method of simplifying a complex Boolean function or expression. The K-Map is basically a graph or a chart which consists of a certain number of adjacent cells. Each cell represents a particular combination of variables in either sum or product form. However, we can use the K-Map for simplifying a Boolean function in any number of variables, but it becomes tedious for functions involving five or more variables. In actual practice, we usually use K-Map for simplification of Boolean functions in upto six variables. A Boolean function in n variables can have ... Read More

In digital electronics, adder and subtractor are the two most basic arithmetic combinational circuits. The adder is a combinational arithmetic circuit used to perform addition of two or more binary numbers. Whereas, the subtractor is a combination arithmetic circuit used to perform subtraction of two binary numbers. Depending on the form in which the addition and subtraction of binary numbers are executed, the adder and subtractor are classified into following types − Serial Adder Parallel Adder Serial Subtractor Parallel Subtractor This tutorial is meant for explaining Parallel Adder and Parallel Subtractor. But before that let us first discuss ... Read More

Any Boolean function or logical expression can be expressed in either canonical/standard sum of products form or canonical/standard product of sums form. The standard sum of products form of a logical expression contains different product terms which are added together, and each product term is referred to as a minterm. On the other hand, the standard product of sums form of a logical expression contains different sum terms which are multiplied together, and each sum term is called a maxterm. In this article, we will discuss about the minterm and max terms. What is Minterm? When a Boolean function or ... Read More

Before focusing on logical expression in SSOP (Standard Sum of Products) form and SPOS (Standard Product of Sum) form, let us have a brief introduction the "Sum of Products" and "Product of Sum" forms. SOP (Sum of Products) Form The SOP or Sum of Products form is a form of expressing a logical or Boolean expression. In SOP, different product terms of input variables are logically ORed together. Therefore, in the case of SOP form, we first logically AND the input variables, and then all these product terms are summed together with the help of logical OR operation. For example ... Read More

K-Map or Karnaugh Map is a graphical method of simplifying Boolean expression. A K-Map composed of an arrangement of adjacent squares or cells, where each cell represent a particular combination of variables in sum or product form. In the K-map method, there is a useful condition namely, Don’t Care Condition, which helps in simplifying a Boolean function. The don’t care condition makes the grouping of variables in K-map easy. In this tutorial, we will understand the "don’t care" concept in K-map reduction with the help of solved examples. Sometimes, in a Boolean expression for certain input combinations, the value of ... Read More

In Boolean algebra, several rules are defined to perform operations in digital logic circuits. Boolean algebra is a tool to perform operation on binary digits, i.e. 0 and 1. These two binary digits 0 and 1 are used to denote FALSE and TRUE states of a digital circuit at input and output ends. Boolean algebra, developed by George Boole, uses 0s and 1s to create truth tables and logic expressions of digital circuits like AND, OR, NOT, etc. which are used to analyze and simplify the complex circuits. There were another English mathematician Augustus De Morgan who explained the NAND ... Read More

A Boolean function can be expressed into two forms namely, Sum of Products (SOP) Form Product of Sums (SOP) Form The SOP (Sum of Products) form is one in which the Boolean function is expressed as the sum of product terms, while in the POS (Product of Sums) form, the Boolean function is expressed as the product of sum terms of the function. But, in the SOP and POS form, each term of the function may not contain all the variables. For example, consider a Boolean function in three variables, $$\mathrm{\mathit{f}\lgroup A, B, C\rgroup=A\overline{B}+\overline{B}C}$$ This is the ... Read More