Homework Assignment #1 – Number Representations
The purpose of this assignment is to let you be familiar and become comfortable with binary
representations which are used heavily in computer organization.
Problem 1 (30 points, 10 points each)
Convert the following decimal numbers into (a) 8bit,
(b) 16bit, and (c) 32bit binary numbers. For negative numbers, use the 2’s complement. State
“overflow” if a number cannot be represented correctly. Hint: You may want to use the sign
extension rule.
1)
45
ten
.
2)
81
ten
.
3)
3,000
ten
.
Solution:
Decimal
number
8bit two’s
complement
binary number
16bit two’s complement binary
number
32bit two’s complement
binary number
45
0010 1101
0000 0000 0010 1101
0000 0000 0000 0000
0000 0000 0010 1101
81
1010 1111
1111 1111 1010 1111
1111 1111 1111 1111
1111 1111 1010 1111
3,000
Overflow
1111 0100 0100 1000
1111 1111 1111 1111
1111 0100 0100 1000
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 Fall '09
 Binary numeral system, Positional notation, Decimal, double precision

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