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CS231 Fall 2010
Homework 2 Solution
1.
(20 pts) Use Kmaps to simplify the following Boolean functions:
a.
F( X, Y, Z ) = XY' + X'Y + X'Z + Y'Z'
F = X' + Y'
b.
F( A, B, C, D ) = ACD + A'BC + BD' + BC'D
F = B + ACD
c.
F( A, B, C, D ) = AB'C + A'B'C' + A'BC'D + B'CD' + C'D'
F = AB'C + A'C' + C'D' + B'D'
d.
F( X, Y, Z ) = ΠM( 0, 2, 3, 5 ) = Σm( 1, 4, 6, 7 )
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View Full Document F = XY + XZ' + X'Y'Z
e.
F( A, B, C, D ) = Σm( 2, 4, 5, 6, 7, 9, 10, 11, 14 )
F =
A'B
+
CD'
+
AB'D
2.
(10 pts) The following Kmaps all attempt to show the function F with don'tcare
conditions d
a.
Which Kmaps have invalid groupings? Explain.
A: Improper grouping (blue). The 1’s can only be wrapped around if they are in the
same column in the outmost blocks.
B: Has a zero
D: Has a grouping that is not a power of 2
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View Full Document b.
What is the minimum sum of products of function F?
F
=
X'Y'Z + WX'Z + YZ' + XZ'
(as shown in Figure c)
OR
F= X'Y'Z + WX'Y + YZ' + XZ'
(when the 1 in the pink rectangle is grouped with the one
on its right, instead of the X)
3.
(12 pts) Use Kmap to obtain a minimal sum of products (MSP) and a minimal product of
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This note was uploaded on 11/08/2010 for the course CS 231 taught by Professor  during the Spring '08 term at University of Illinois at Urbana–Champaign.
 Spring '08
 
 Computer Architecture

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