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

  $\text{Decimal = }\left(\text{sign}\right)\left(\text{1}\text{.fraction}\right){\text{ * 2}}^{\text{exponent - bias}}$

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