- published: 07 Jan 2015
- views: 43229
In mathematics, a (finitary) Boolean function (or switching function) is a function of the form ƒ : Bk → B, where B = {0, 1} is a Boolean domain and k is a non-negative integer called the arity of the function. In the case where k = 0, the "function" is essentially a constant element of B.
Every k-ary Boolean formula can be expressed as a propositional formula in k variables x1, …, xk, and two propositional formulas are logically equivalent if and only if they express the same Boolean function. There are 22kk-ary functions for every k.
A Boolean function describes how to determine a Boolean value output based on some logical calculation from Boolean inputs. Such functions play a basic role in questions of complexity theory as well as the design of circuits and chips for digital computers. The properties of Boolean functions play a critical role in cryptography, particularly in the design of symmetric key algorithms (see substitution box).
Boolean functions are often represented by sentences in propositional logic, and sometimes as multivariate polynomials over GF(2), but more efficient representations are binary decision diagrams (BDD), negation normal forms, and propositional directed acyclic graphs (PDAG).
Implementation of Boolean Function using Multiplexers
Boolean Simplification
IMPLEMENTATION OF BOOLEAN FUNCTIONS IN SUM OF PRODUCT FORM BY NAND GATES(DIGITAL SYSTEM-48)
EE 2381 Boolean Functions with MUX
Boolean function example (C++ programming tutorial)
TRUTH TABLE OF BOOLEAN FUNCTIONS (DIGITAL SYSTEM-10)
Digital Electronics -- Boolean Algebra and Simplification
Boolean Functions by Raj Kumar Thenua (Hindi / Urdu)
Digital Logic (DLD) : boolean algebra and minimization of boolean function
Lecture - 8 Boolean Function Minimization
IMPLEMENTING BOOLEAN FUNCTIONS BY MULTIPLEXER(DIGITAL SYSTEM-50)
IMPLEMENTING BOOLEAN FUNCTIONS(OR COMBINATIONAL CIRCUITS) BY DECODER(DIGITAL SYSTEM-45)
GATE 1993 ECE Realization of 4 variable boolean function using 8 to 1 Multiplexer
Expressing Boolean Functions with MUXs