Chapter 03 - Boolean Algebra II-2x2(1)

Instead we will use the distributive laws to simplify

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Unformatted text preview: Instead, we will use the distributive laws to simplify the process. Example (3-4), p. 63 The same theorems that are useful for multiplying out expressions are useful for factoring. By repeatedly applying (3-1), (3-2), and (3-3), any expression can be converted to a product-of-sums form. Exclusive-OR and Equivalence Operations The exclusive-OR operation ( ) is defined as follows: The equivalence operation ( ) is defined by: We will use the following symbol for an exclusiveOR gate: Section 3.2, p. 64 The following theorems apply to exclusive OR: We will use the following symbol for an equivalence gate: Section 3.2, p. 65 Example 1: Because equivalence is the complement of exclusive-OR, an alternate symbol of the equivalence gate is an exclusive-OR gate with a complemented output: By (3-6) and (3-17), F = [(A′B)C + (A′B)′C′ ] + [B′(AC′) + B(AC′)′ ] = A′BC + (A + B′) C′ + AB′C′ + B(A′ + C) = B(A′C + A′ + C) + C′(A + B′ + AB′) = B(A′ + C) + C′(A + B′) Example 2: The e...
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This document was uploaded on 03/16/2014 for the course EE 316 at University of Texas at Austin.

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