Chapter 2.3, Problem 2.39PP

Program Plan Intro

Generating code for the expression:

Assume the task of creating code for the expression “$\text{x * K}$” for some constant “K”.

• The compiler can express the binary representation of “K” by using as an alternating sequence of zeros and ones.
• The expression is represented by $\left[\left(\text{0}\mathrm{....}\text{0}\right)\left(\text{1}\mathrm{....}\text{1}\right)\left(\text{0}\mathrm{...}\text{0}\right)\mathrm{......}\left(\text{1}\mathrm{....}\text{1}\right)\right]$.
• Consider a run of ones from bit position “n” down to bit position “m”.

Compute the effect of bits on the product:

User can determine the effect of bits on the product using two different forms such as Form A and Form B.

• Form A:
  • The form A is represented by $\left(\text{x<<n}\right)\text{+}\left(\text{x<<}\left(\text{n}\text{-}\text{1}\right)\right)\text{+}\mathrm{....}\text{+}\left(\text{x<<m}\right)$.
• Form B:
  • The form B is represented by $\left(\text{x<<}\left(\text{n}\text{+}\text{1}\right)\right)\text{-}\left(\text{x<<m}\right)$.