Found 10 Articles for Functions

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

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

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

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

When a Boolean expression is represented as a product of sum terms, it is called POS (Product of Sums) form. In POS form, each sum term of the expression may not contain all the variables. On the other hand, when the Boolean expression is represented as a product of sum terms, where each sum term contains all the variables of the function, it is called Standard Product of Sums (SPOS) form. In the Standard POS form, each sum term of the Boolean expression is called a maxterm. Now, let us discuss the expansion of a Boolean expression in POS form ... Read More

When a logical expression or Boolean function is expressed as a sum of minterms or as a product of maxterms, then it is called the canonical form of the expression or function. A canonical form of the Boolean expression is also known as standards form, i.e. Standard Sum of Products (SSOP) Form and Standard Product of Sums (SPOS) Form. The canonical form of a Boolean function involves minterms and maxterms. A minterm is a product term which contains all the variables of the Boolean function either in complemented or un-complemented form. A maxterm is a sum term which ... Read More

In mathematics, functions play a vital role in describing and modeling various phenomena. A function is a rule that assigns a unique output value to each input value. The set of input values is called the domain, and the set of output values is called the range. However, in some cases, the range is not the same as the codomain, which can lead to confusion. In this essay, we will explore the difference between codomain and range. Codomain of a Function The “codomain” of a function or relation is a set of values that might possibly come out of it. ... Read More

Multiple processes that are running on various machines or nodes and interacting with one another to accomplish a single objective makeup distributed systems. In these systems, it's crucial to make sure that only one process is able to utilize a shared resource at once to prevent conflicts and data inconsistencies. One way to make sure that only one function is using a shared resource at once is through the use of mutual exclusion and Lamport's Algorithm is one of many accessible mutual exclusion algorithms. Lamportís Algorithm A centralized mutual exclusion algorithm called Lamport's Algorithm employs timestamps to determine the sequence ... Read More

Introduction Due to the non-linearity that can introduce towards the output of neurons, activation functions are essential to the functioning of neural networks. Sigmoid and tanh are two of the most often employed activation functions in neural networks. Binary classification issues frequently employ the sigmoid function in the output layer to transfer input values to a range between 0 and 1. In the deep layers of neural networks, the tanh function, which translates input values to a range between -1 and 1, is frequently applied. The usage of either function relies on the particular needs of the issue being handled ... Read More

Introduction The cell surface is the outermost layer of the cell that interacts with the external environment. It is a dynamic and complex structure composed of various biomolecules, including lipids, proteins, and carbohydrates. The cell surface plays a crucial role in communication between cells and their environment, and this communication is mediated by cell surface receptors. Cell surface receptors are transmembrane proteins that bind to specific molecules in the extracellular environment and transmit signals to the intracellular environment to elicit cellular responses. In this tutorial, we will explore the different types of cell surface receptors, their functions, and the ... Read More