Let's start this tutorial with a basic introduction of 8:1 multiplexer before moving on to cover how a three variable logic function can be implemented using an 8:1 multiplexer. Introduction to 8:1 Multiplexer A multiplexer (or MUX) is a digital logic circuit that accepts multiple data inputs and allows only one of them at a time to pass through the output line. Hence, multiplexer is also known as data selector. In other words, a multiplexer is a digital circuit which Based on the number of input data lines, there are several types of multiplexers. But, this article is meant ... Read More

Simplification is an approach in which a Boolean expression is minimized or reduced into an equivalent expression by using some Boolean identities. Boolean algebra is a mathematic applied to binary number system. It was developed by George Boole, an English mathematician, to simplify complex logical operation to their simplest form. The simplification of a Boolean function is important because it reduces the number of logic devices/gates required to implement a logic function. This in turn reduces the hardware cost and complexity of the circuit. Also, it increases the reliability of the system. In this tutorial, we will understand the ... Read More

In digital electronics, the binary adder is a combinational logic circuit which performs the addition of two or more binary digits. The binary addition is performed based on the Boolean algebraic laws of addition, i.e., $$0+0=0$$ $$0+1=1$$ $$1+0=1$$ $$1+1=0$$ Binary adders are classified into two types namely, serial binary adder and parallel binary adder. In this tutorial, we will discuss serial binary adder, its definition, logic circuit diagram, and operation. So, let us start with basic introduction of serial binary adder. What is a Serial Binary Adder? A serial binary adder is a binary adder circuit which is used to ... Read More

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