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

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

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

Electronic logic conventions are the sets of rules followed while designing a digital logic system or device. These conventions are adopted due to their different characteristics observed by several experiments. The use of electronic logic conventions, makes the implementation process of a digit system easy and smooth. Also, a standardization is achieved in the design. This tutorial is entirely meant for explaining different electronic logic conventions used in digital system implementations. As we know, the digital systems are implemented in binary number system due to some technical and economic reasons. The binary number system follows Boolean’s rules to perform arithmetic ... Read More

Dyson manufactures two upright vacuum cleaner models, the DC25 and the DC25 Animal. Although they have many similarities, there are certain variances between them that set them apart. The DC25 Animal is a pet-specific vacuum cleaner, whereas the DC25 is a general-purpose vacuum cleaner. Read this article to find out more about Dyson DC25 and DC25 Animal and how they are different from each other. What is Dyson DC25? The Dyson DC25 upright vacuum cleaner was released by Dyson in 2008. Because of its tremendous suction, innovative technology, and ease of use, it has since become a favourite choice ... Read More

Valet and Valet Plus are parking services provided by various companies or establishments. The primary difference between Valet and Valet Plus is the level of service and convenience provided. Valet parking is a service in which a customer hands over their vehicle for parking to a valet attendant, whereas valet plus is a premium version of valet parking that includes additional services such as car detailing and maintenance. Read this article to find out more about Valet and Valet Plus and how they are different from each other. What is Valet? A valet parking service is a type of ... Read More