09--Sums of Products and Products of Sums

09--Sums of Products and Products of Sums - Sums of...

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Sums of Products, Products of Sums Sum of Products Consider the following digital network (function): A B C F(A, B, C) 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 This can be converted into the following algebraic expression: F(A,B,C) = A'BC' + A'BC + AB'C' + ABC This form of an equation—a series of AND terms (products) connected into an OR (added) is referred to  as a SUM OF PRODUCTS equation. This equation can easily be drawn. /* Draw it */ It is NOT necessarily the simplest circuit but it is the easiest to derive from the truth table. Sum of Products  equation in which each AND term contains ALL input variables is said to be in  Normal Form  (or  canonical form ) and each term is called a  minterm. Minterm:  an AND term that contains all input variables. A function equivalent to the previous one: F(A, B, C) = A'B + AB'C' + BC To convert it into normal form, multiply terms with missing variables by 1: F(A, B, C) =  (A'B)*1   +   AB'C'   +   (1)BC

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This document was uploaded on 02/29/2012.

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09--Sums of Products and Products of Sums - Sums of...

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