# Boolean functions

## Introduction

A mathematical expression consisting of Boolean variables combined using the Boolean algebra operators: logical addition (OR), multiplication (AND) and negation (NOT) is a Boolean function.

## Mathematical definition

If $k$ is the number of Boolean variables of the function, then the function $f(x_1,\ldots,x_k)$ and its domain and codomain are defined as $f:{0,1}^k\rightarrow{0,1}$

## Important concepts

The following is a list of definitions for fundamental concepts used in Boolean functions:

• Literal: A logic variable or its complement $(x,\overline{x},y_0,\ldots)$.
• Product term: An expression where literals are combined by the logical AND operator $(x\overline{y}z,\ldots)$.
• Sum term: An expression where literals are combined by the logical OR operator $(y+\overline{z},\ldots)$.
• Normal term: A (product or sum) term without repeated variables.
• Sum of Products (SoP): A sum of product terms $(\overline{x}+xwz+x\overline{y})$.
• Product of Sums (PoS): A product of sum terms $((x+y+z)(z+\overline{w})(z+\overline{x}))$.

• Section 3.2 “Switching functions” in .
• Section 1.3 “Boolean Functions” in .
• Chapter 3 “Boolean Algebra and Logic” in .
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1. Every Boolean Function can be expressed as ________ ?
1. Algebraic expression
• Laplace expression
• Binomial expression
2. SOP (Sum of Product) is referred as ________ ?
1. (x+xwz+xy)
• ((x+y+z)(z+w)(z+x))