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Unformatted text preview: Instead, we will use the distributive laws to
simplify the process. Example (34), p. 63 The same theorems that are useful for multiplying out
expressions are useful for factoring. By repeatedly
applying (31), (32), and (33), any expression can be
converted to a productofsums form. ExclusiveOR and Equivalence Operations The exclusiveOR 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 exclusiveOR,
an alternate symbol of the equivalence gate is an
exclusiveOR gate with a complemented output: By (36) and (317),
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.
 Spring '08
 Brown

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