Chapter 2.1, Problem 2.16PP

Program Plan Intro

Shift operations in “C”:

In “C”, user can shifting bit patterns to the left and to the right using “shift” operations.

• Here “x” is an operand which having bit representation $\left[{\text{x}}_{\text{w-1}}\text{,}{\text{x}}_{\text{w-2}}\text{,}\mathrm{.......}{\text{,x}}_{\text{0}}\right]$, the “C” expression “x << k” produce a result with bit representation $\left[{\text{x}}_{\text{w-k-1}}\text{,}{\text{x}}_{\text{w-k-2}}\text{,}\mathrm{.......}{\text{,x}}_{\text{0}}\text{,}\text{0,}\mathrm{.......}\text{,0}\right]$
• The left shift operation is denoted by the symbol “<<”.
  • For example, “x << k” means “x” is shifted “k” bits to the left, reducing “k” most significant bits and filling the right end with “k” zeros.
• The right shift operation is denoted by the symbol “>>”.
  • For example, “x >> k” means “x” is shifted “k” bits to the right
  • Generally machines provides two types of right shift.
    • Logical right shift:
      • In this operation, the left end is filled with “k” zeros and its result becomes $\left[\text{0,}\mathrm{..........}{\text{0,x}}_{\text{w-1}}\text{,}{\text{x}}_{\text{w-2}}\text{,}\mathrm{.......}{\text{,x}}_{\text{0}}\right]$.
    • Arithmetic right shift:
      • In this operation, the left end is filled with “k” repetitions of the most significant bit and its result become $\left[{\text{x}}_{\text{w-1}}\text{,}\mathrm{.......}{\text{,x}}_{\text{w-1}}{\text{,x}}_{\text{w-1}}{\text{,x}}_{\text{w-2}}\text{,}\mathrm{......}{\text{x}}_{\text{k}}\right]$.