Computer Systems: A Programmer's Perspective Plus Mastering Engineering With Pearson Etext -- Access Card Package (3rd Edition)
Computer Systems: A Programmer's Perspective Plus Mastering Engineering With Pearson Etext -- Access Card Package (3rd Edition)
3rd Edition
ISBN: 9780134123837
Author: Randal E. Bryant, David R. O'Hallaron
Publisher: PEARSON
Question
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Chapter 2.1, Problem 2.2PP
Program Plan Intro

Decimal and hexadecimal representation of different powers of 2:

  • When a value “x” is a power of 2, that is x = 2n for some nonnegative integer n.
    • Here, the binary representation of x is basically “1” followed by n zeros.
  • The hexadecimal digit is represented by “4” zeros. Hence, the format for “n” is “i + 4j”.
  • From “i + 4j” format, where 0i3, user can write “x” with a leading hex digit of 1, 2, and 3 and then followed by “j” hexadecimal digits.
    • If “i = 0”, then hex digit is “1”.
      • If “i = 1”, then hex digit is “2”.
      • If “i = 2”, then hex digit is “4”.
      • If “i = 3”, then hex digit is “8”.

Example:

The example for decimal and hexadecimal representation of power of “2” is shown below:

Here assume x = 2048 = 211.

Now, write the “n” value as the format of “i + 4j” that is “3 + 4.2”.

  • From the given format, the “i” value of “3” in hexadecimal is “8”. Then “j” is “2” so, after “8” two 0’s followed. Hence, the hexadecimal value is “0x800”.

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Chapter 2 Solutions

Computer Systems: A Programmer's Perspective Plus Mastering Engineering With Pearson Etext -- Access Card Package (3rd Edition)

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