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CS 15-213, Fall 2006
Exam 1
Wednesday October 4, 2006
Instructions:
•
Make sure that your exam is not missing any sheets, then write your full name and Andrew login ID
on the front.
•
Write your answers in the space provided below the problem. If you make a mess, clearly indicate
your final answer.
•
The exam has a maximum score of 56 points.
•
The problems are of varying difficulty. The point value of each problem is indicated. Pile up the easy
points quickly and then come back to the harder problems.
•
This exam is OPEN BOOK. You may use any books or notes you like. Calculators are allowed, but
no other electronic devices. Good luck!
1 (8):
2 (8):
3 (8):
4 (6):
5 (8):
6 (8):
7 (10):
TOTAL (56):
Page 1 of 10

Problem 1. (8 points):
Assume we are running code on an IA32 machine, which has a 32-bit word size and uses two’s complement
arithmetic for signed integers. Consider the following definitions:
int x = foo();
unsigned ux = x;
Fill in the empty boxes in the table below. For each of the C expressions in the first column, either:
•
State that it is true of all argument values, or
•
Give an example where it is not true.
Puzzle
True / Counterexample
x < 0
⇒
(x
*
2) < 0
False (TMin)
x > 0
⇒
(x+1) > 0
x > 0
⇒
(˜x + 2) <= 0
(x>>31) == -1
⇒
x < 0U
x < 0
⇒
((x ˆ x>>31) + 1) > 0
((x>>31)+1) == (x>=0)
x >= 0
⇒
((int)(ux >> 31) + ˜0) == -1
-(x | (˜x + 1)) > 0
Page 2 of 10

Problem 2. (8 points):
Consider the following 5-bit floating point representations based on the IEEE floating point format. This
format does not have a sign bit – it can only represent nonnegative numbers.
•
There are
k
= 3
exponent bits. The exponent bias is 3.
•
There are
n
= 2
fraction bits.
Numeric values are encoded as a value of the form
V
=
M
×
2
E
, where
E
is exponent after biasing, and
M
is the significand value. The fraction bits encode the significand value
M
using either a denormalized
(exponent field 0) or a normalized representation (exponent field nonzero).
Below, you are given some decimal values, and your task it to encode them in floating point format. If

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