Chapter 3, Problem 3RQ

Explanation of Solution

Excess notation:

• Signed integer can be represented with a fixed number of bits using the format known as excess notation.
• The range of ordinary binary numbers are divided by this format and it uses lower half for negative values and upper half for positive values...

Explanation of Solution

Twos complement notation:

• In base two numbering system, the complement of “1” is “0” and the complement of “0” is ‘1”.
• To find complement of a bit string, “1” is substituted for all values of ȁ...

Explanation of Solution

The purpose of twos complement notation:

• Digital electronic circuitry uses twos complement notation for the following reasons;
  • The sign is represented using the leftmost bit.
  • It uses fixed number of bits.
  • It requires only two logic circuits to perform single bit addition...

Explanation of Solution

Representation of integer value:

• Positive integers are represented as ordinary binary values but twos complement of negative integers are represented by adding one to the complement of nonnegative integers.
• Example:
  • The twos complement notation for the nonnegative integer “$6_{10}$” is represented using four bits is “$0110$”.
  • Twos complement notation for the negative integer “$-6_{10}$” is represented by adding one to the complement of positive integer.

$\begin{array}{c}\text{Twos}\text{complement}\text{of}-{\text{6}}_{}\end{array}$