CS 354, version A
Fall 2005 		Answer Key
Exam 1 Solution

No electronic devices may be used while taking this exam. Examples of devices not allowed are calculators, pagers, cell phones, wrist calculators/computers, laptop computers, pocket computers. Each student is allowed one 8.5 by 11 inch sheet of paper with handwritten notes. The notes may be on both sides of the paper.

Show all work, and do any/all calculations on the exam. Extra scratch paper may not be used.

Exam Score
Q1 = _____ /   4
Q2 = _____ /   6
Q3 = _____ /   6
Q4 = _____ / 12
Q5 = _____ /   8
Q6 = _____ / 10
Q7 = _____ /   8
Q8 = _____ /   4
Total = _____ / 58		 




Question 1 (4 points)



For the run length encoding program you wrote (Assignment 1):
if the following string is the complete contents of a file
that is to be compressed (encoded) by the program,
how many character-sized items will be in the resulting
file?

aaaabbb?????x




Answer: 8




Question 2 (6 points)



A Unix command line appears as

% a.out start 1 stop 100


Diagram argc and argv
as they are given to a C program.


argc is 5

           -----
argv ----->| --|---> "a.out"
           -----
           | --|---> "start"
           -----
           | --|---> "1"
           -----
           | --|---> "stop"
           -----
           | --|---> "100"
           -----





Question 3 (6 points)


Write the output from this C program to the right
of the source code.


#include <stdio.h>

main()
{
   int a = 3;              ----------------------------
   int b = 8;              | b equals c
   int c = 12;             | pointers not the same
   int *ap;                | equal
   int *bp;
   int *cp;

   ap = &a;
   bp = &b;
   cp = &c;

   ap = bp;
   *bp = *cp;

   if ( b == c ) {
      printf("b equals c\n");
   } else {
      printf("b does not equal c\n");
   }

   if ( bp == cp ) {
      printf("pointers same\n");
   } else {
      printf("pointers not the same\n");
   }

   if ( (*ap) == c ) {
      printf("equal\n");
   } else {
      printf("not equal\n");
   }
   return(0);
}





Question 4 (12 points)


Identify the six steps of the instruction fetch and execute cycle
in their proper order:

    

  1. )
instruction fetch

     
    

  2. )
PC update

     
    

  3. )
decode

     
    

  4. )
get operand(s)

     
    

  5. )
do the operation

     
    

  6. )
store result(s)





Question 5 (8 points)


Part A
What decimal value is represented by the 8-bit,

two's complement representation 11101100?



Answer: -20

This is a negative integer, so take the two's complement to find
out its absolute value:
00010011 + 1 = 00010100  is 16+4= 20.



Part B
What is the 8-bit, two's complement representation

for the decimal value 65?



Answer: 01000001

65 is 64+1
1000001 in binary.
The two's complement value in 8 bits zero extends this by 1 bit.





Question 6 (10 points)


Part A
Give the decimal value 20.3 in base 4.
Show any repeating digits by placing a bar over those digits that repeat.


Following the given algorithm:
      Q  R
20/4  5  0
 5/4  1  1
 1/4  0  1  Therefore 20 (base 10) = 110 (base 4)

Again, following a given algorithm:
.3 * 4   1.2
.2 * 4   0.8
.8 * 4   3.2
.2  (and notice that it repeats the last 2 digits)

                       __
20.3 (base 10) is 110.103 (base 4)
(where only the 03 portion repeats)






Part B
Give the octal value 60.2 in decimal.
Show any repeating digits by placing a bar over those digits that repeat.


This is
6 * 8^1 + 0 * 8^0 + 2 * 8^(-1)
  48    +   0     +   2/8

  Answer: 48 1/4 or 48.25





Question 7 (8 points)


Give the  IEEE single precision floating point representation 
(in hexadecimal) for the decimal value

   -1026.75.



1026 is 1024 + 2 or 2^10 + 2
In binary,  10000000010

.75 is .11 in binary

Put the 2 parts together to get
  10000000010.11   *   2^0

Move the radix point 10 places to the left to get
  1.000000001011   *   2^10

The exponent field is unsigned of 10+127 (or 9+128)
   10001001

Putting the pieces into their fields (not representing the hidden bit):

  S  E           F
  1  10001001    00000000101100000000000

Respacing to get hexadecimal easily:
  1100 0100 1000 0000 0101 1000 0000 0000

  0x c4805800






Question 8 (4 points)


Given n bits, what range of integers can be
represented in two's complement representation?


  -(2^(n-1)) to  + 2^(n-1)  - 1