Chapter 2.2, Problem 2.23PP

A.

Program Plan Intro

• From the given two functions, the expressions are common program “idioms” for extracting values from a word in which multiple bit fields have been packed.
• From the question, the two given function uses shift operations.
  • In “fun1”, the shifts are implemented on unsigned variable “word” and hence are “logical”.
    • In this function, first performs left shift operation and then performs logical right shift operation.
  • In “fun1”, the shifts are implemented after casting “word” to “int” and hence are “arithmetic”.
    • In this function, first performs left shift operation and then performs arithmetic right shift operation.

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 provide 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 $\left[{\text{x}}_{\text{w-1}}\text{,}\mathrm{.......}{\text{,x}}_{\text{w-1}}{\text{,x}}_{\text{w-1}}{\text{,x}}_{\text{w-2}}\text{,}\mathrm{......}{\text{x}}_{\text{k}}\right]$.

B.

Explanation of Solution

Useful computation for given two functions:

• The function “fun1” extracts a value from the low-order 8 bits of the argument.
  • This function producing result an integer ranging between “0” and “255”...