Shannon expansion

Shannon expansion

Shannon expansion refers to a mathematical technique used to represent Boolean functions in a specific form. It has several variations, including the generalized Shannon expansion for multiple-valued logic functions, the arithmetic analog of Shannon expansion for representing Boolean functions in word-level form, and the information-theoretical form of Shannon expansion for computing Boolean functions in terms of information.From: Introduction to Logic Design [2019]

Introduction

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Published in Vlad P. Shmerko, Svetlana N. Yanushkevich, Sergey Edward Lyshevski, Computer Arithmetics for Nanoelectronics, 2018

Vlad P. Shmerko, Svetlana N. Yanushkevich, Sergey Edward Lyshevski

Shannon expansion provides a model for the multiplexing of Boolean functions, which enables representation of the Boolean function for further implementation as a logic network of universal gates such as multiplexers. Multiplexing can be implemented:

Characterization of Test Sets for Multiple Faults in Combinational Network

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Journal Information

Published in IETE Journal of Education, 2021

Pramode Ranjan Bhattacharjee

The first-order Shannon expansion [16] of a Boolean function with respect to the variable is given by where 1 and 0 shown in the middle correspond to the input . Also, it may be noted that, here and denote the first- order Shannon coefficients for expansion with respect to the variable . These two coefficients constitute the first-order Shannon spectrum of the Boolean function for expansion with respect to the variable .

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Introduction

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