Reed Muller Canonical Form

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Reed Muller Canonical Form

Shardul Goel
Roll no – 10104EN003
B.Tech, Third Year
Electrical Engineering
IIT(BHU), Varanasi

Abstract— This term paper gives a description of the well known Reed Muller canonical form for specifying a logical function. It aims at explaining the Reed Muller form and analyze its importance. It also deals with the methods to convert a given logical function into this form.

Introduction
A logic function may be represented in a variety of forms and implemented using a multitude of circuits. A particularly interesting and useful form of representation is the canonical form of representation. A logical function is said to be in canonical form if it is expressed as sum of minterms or as a product of maxterms. A logical function may also be implemented as a multi level tree of XOR gates. Such a type of representation (in terms of XOR gates) is highly advantageous and is the basis for the Reed Muller Canonical form.

Definition
A logical function is said to be in the Reed Muller canonical form if it is expressed as an exclusive OR of the products of uncomplemented variables. A simple example can be
f(AB) = A’B + AB’ can be written as AB.

Advantages of reed muller canonical form

1) The problem with the SOP or POS forms of representation is that each of the variables can be present in complemented or uncomplemented form so that there are effectively twice the number of primary input variables in the expression. This problem is not there in the Reed Muller form

as the variables must be present in the uncomplemented form only. 2) A function implemented in the Reed Muller form is fully testable with a finite number of discrete tests. For a function of n variables the total number of input combinations required for exhaustive testing is 2n. As the number of variables increases it becomes impossible to test the circuit using this exhaustive conventional approach. If we apply the restriction that only...
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