Representing Integers and Manipulating Bits

Goals

This lab provides practice in working with data at the bit level in C. Specific work involves the representation of integers, the manipulation of bits in C, and the use of unions in C to view bit patterns in multiple ways.

Background

The C programming language contains the following bitwise operations:

The text (page 53) shows the precedence of these operations together with the more familiar arithmetic and logical operations.

Binary Representation of Integers

The first half of this lab examines the binary representation of integers, using a program to display the representation of various integers. More specifically, program ~walker/c/data-rep shows the internal bit representation of numbers specified by the user. This part of the lab asks you to run this program, focusing on the numbers and their representation. The second part of the lab examines the program itself.

1. Write the integers ± 1, ± 2, ± 3, ± 6, ± 9 using sign/magnitude notation, ones complement notation, and twos complement notation.

2. Run program ~walker/c/data-rep to determine the internal representation of the integers from part 1, as actually stored on PC/Linux computers.

   1. For positive integers, check that the bit patterns correspond to the binary representations you calculated.
   2. For negative integers, determine which notation is used on the PC/Linux computers. Be sure you can justify your answer by citing output you obtained.

Unions and Bitwise Processing in C

This part of the lab examines the program data-rep.c, which allowed the experimentation done above. Copy this program (~walker/c/data-rep.c) to your account, examine the C code itself, and answer the following questions on the program.

3. Review program data-rep.c carefully.

   1. What can be stored or accessed in a DATA type?
   2. A typedef statement allows the type union DATA to be identified more simply as a data type. Explain what data may be stored in variable d and how that data can be accessed.

4. The main part of this program consists of a single loop.
   1. What is the significance of the number 1 in the while (1) expression?
   2. Under what circumstances does the program terminate, and how is this made to happen?
   3. [Note that continue is used in place of break in the default option, so execution at that spot will jump back to the top of the loop rather than continuing with the printing that follows.]

5. Explain how numbers are set in options 0, F, and I.

6. Why is the number -1 used for option 1?

7. After each number is set, its value is printed using several representations. While the printf statements are straight forward, the printBitGroups function may require some thought. The first use of this function comes from the call printBitGroups (d, 1). Using bitGroups as 1, trace the execution of printBitGroups.
   1. Identify the initial values of value, mask and iterations. (Variable a is an array of integers, with subscripts between 0 and 31.)
   2. Describe the final value of variable mask after the first loop terminates, and explain how that bit pattern is achieved.
   3. Explain what processing is done in the second loop; what are the final values placed in the a array, and how are these values determined.
   4. Why do you think the value variable is declared as d.integer, rather than using d.integer directly in the second loop of printBitGroups.

8. Explain the purpose of the call printBitGroups (d, 4), and discuss how this purpose is achieved.
   1. What is the purpose of the number 4 in this call?
   2. Describe the final value of variable mask after the first loop terminates, and explain how that bit pattern is achieved.
   3. Explain what processing is done in the second loop; what are the final values placed in the a array, and how are these values determined.

9. Write (in English) appropriate pre- and post-condidtions for function printBitGroups. These conditions should be inserted as comments to follow the function's header, but they need NOT be checked in the code using assert statements or other executed tests.

10. Add a menu option to this program, so that the integer value of variable d is changed to its ones complement.

11. Add a menu option to this program that begins with the value in variable d and successively toggles successive bits of the variable -- printing the binary, hexadecimal, integer, and float values of the results in a table. Toggling of the bits should progress from left to right. Thus, the output might have the form:
    
    

    binary	hexadecimal	integer form	float form
    00000000000000000000000000000000	00000000	0	0.0
    10000000000000000000000000000000	80000000	-2147483648	-0.0
    01000000000000000000000000000000	40000000	1073741824	2.0
    ...

Work to turn in

• Commentary for steps 1-8, with no commentary needed for 4c.
• A program listing, with appropriate test runs and comments on correctness, for steps 9, 10, and 11.
  • One program listing is adequate to cover steps 9 to 11.
  • As with all programs for this course, please follow the course's specified format for submitting assignments.

This document is available on the World Wide Web as

     http://www.cs.grinnell.edu/~walker/courses/201.sp05/lab-integers.shtml

created September 11, 2001 last revised February 3, 2005
For more information, please contact Henry M. Walker at walker@cs.grinnell.edu.