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Department of Electrical and Computer Engineering
University of Minnesota
EE 2301
Fall 2009
Introduction to Digital System Design
L. L. Kinney
Discussion II Solutions
Sept. 17 & 18: Topics are arithmetic with 1 and 2’s complement numbers, Boolean algebra
identities, switch networks, canonical expressions and tables of combinations.
1.
a)
Represent the following decimal numbers as hexadecimal numbers using 15’s (1’s)
complements:
45, 83, 45 and 83.
b)
Using the hexadecimal representations from part a) perform the following operations:
45 + (83), (45) + (83), (45) + (83).
Verify that the sum is correct or else show that
overflow occurs.
c)
Repeat Part a) using 16’s (2’s) complement numbers.
d)
Repeat Part b) for the 16’s complement numbers.
a)
45
10
= 2D
16
, 83
10
= 53
16
, 45
10
= D2
16
, 83
10
= AC
16
b)
2D
16
+ AC
16
= D9
16
= (38
10
), D2
16
+ 53
16
= 26
16
= (38
10
), D2
16
+ AC
16
=
7F
16
= (127
10
) = (128
10
) overflow
c)
45
10
= 2D
16
, 83
10
= 53
16
, 45
10
= D3
16
, 83
10
= AD
16
d)
2D
16
+ AD
16
= DA
16
= (38
10
), D3
16
+ 53
16
= 26
16
= (38
10
), D3
16
+ AD
16
=
80
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This note was uploaded on 12/20/2009 for the course EE 2301 taught by Professor Larrykinney during the Fall '09 term at Minnesota.
 Fall '09
 LarryKinney

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