Introduction to Computing Systems: From Bits & Gates to C & Beyond
Introduction to Computing Systems: From Bits & Gates to C & Beyond
3rd Edition
ISBN: 9781260424751
Author: PATT, Yale
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 2, Problem 52E

Explanation of Solution

Hexadecimal number conversion

  • For converting hexadecimal number “x434F4D50” into unsigned binary, then each hexadecimal digit is represented as a 4-bit binary string.
  • Hence the unsigned binary number of “x434F4D50” is

    0100 0011 0100 1111 0100 1101 0101 0000.

  • The unsigned binary number of “x55544552” is

    0101 0101 0101 0100 0100 0101 0101 0010

  • The 1’s compliment of a hexadecimal number is calculated by converting the binary string into its one’s compliment and inverting all the bits that is 0 to 1 and 1 to 0.
  • Hence the 1’s compliment of “x434F4D50” is

    1011 1100 1011 0000 1011 0010 1010 1111

  • The 1’s compliment of “x55544552” is

    1010 1010 1010 1011 1011 1010 1010 1101

  • The 2’s compliment of a number is calculated by inverting all bits and then adding number 1 to all bits.
  • Hence the 2’s compliment of “x434F4D50” is

    1011 1100 1011 0000 1011 0010 1011 0000

  • The 2’s compliment of “x55544552” is

    1010 1010 1010 1011 1011 1010 1010 1110

  • For converting the binary string into IEEE format, the binary string is divided into three parts that is sign, exponent and fraction.
  • The exponent and fraction part is then converted into decimal.
  • The IEEE 754 floating point is calculated by

    Decimal = (sign)(1.fraction) * 2exponent - bias

  • For converting hexadecimal number “x434F4D50” into ASCII string,
    • The binary value 01000011 represents hexadecimal 43

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