ic
Section 8.2 Logic Networks
659
x 1
x 2
x 3 f( x 1 , x 2 , x 3 )
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23. a. Show that the two Boolean expressions
(x 1 + x 2 )(x 1 ′ + x 3 )(x 2 + x 3 )
and
(x 1 x 3 ) + (x 1 ′x 2 )
are equivalent by writing the truth function for each.
b. Write the canonical sum-of-products form equivalent to the two expressions of part (a).
c. Use properties of a Boolean algebra to reduce one of the expressions of part (a) to the other.
24. The accompanying figure shows an unprogrammed PLD for three inputs, x 1 , x 2 , and x 3 . Program this PLD
to generate the truth functions f 1 and f 3 represented by
f 1 : x 1 x 2 x 3 + x 1 ′x 2 x 3 ′ + x 1 ′x 2 ′x 3
f 3 : x 1 x 2 ′x 3 ′ + x 1 ′x 2 ′x 3 + x 1 ′x 2 ′x 3 ′
f 1
x 3
x 2
x 1
f 2
f 3
f 4
Input
Output