Name:
Student ID #
CSE 110 Homework 2 — ANSWER KEY
Due:
Monday, October 18, at the start of class. Homework 2 should be turned in
on paper
.
This assignment is worth a total of 12 points.
You must show all work in order to receive any credit
for your solutions.
1.
Decode the following bit pattern using the following Foatingpoint format: 1 sign bit, 8 bits of exponent
(the bias is 127), and 23 bits of mantissa. (3 points)
1100 0010 0100 1011 0000 0000 0000 0000
Sign bit:
1
Exponent:
10000100
Mantissa:
10010110000000000000000
Exponent = 10000100 = (128 + 4) = 132  127 (the bias) = 5
Restored mantissa: 1.10010110000000000000000 x 2
5
Shifting the binary point back to the right, we get
110010.11000.
..
Translating back to base 10, we get
(32 + 16 + 2) = 50
(0.5 + 0.25) = 0.75
50.75
Applying the sign bit (1), we get the Fnal result: 50.75
Assign 0.5 point for each of the following steps:
0.5 Breaking the original number into sign, exponent, and mantissa Felds
0.5 Correctly translating the exponent and subtracting the bias amount
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 Fall '08
 SHAUNAKPAWAGI
 Addition, Binary numeral system, sign bit

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