Chapter 2.3, Problem 2.38PP

Program Plan Intro

LEA instruction:

• The “LEA” instruction is provided to support pointer arithmetic.
  • The “C” compiler can perform multiplication by constant factors with “LEA” instruction.
• This instruction can perform computations of the form $\text{(a<<k)}\text{+}\text{b}$
  • Here, the value of “k” is 0, 1, 2, or 3 and value of “b” is “0” or some other program value.

Unsigned multiplication by a power of “2”:

Consider the variables “x” and “k” with unsigned values “x” and “k” in the range $\text{0}\le \text{k}\text{<}\text{w}$

Then the “C” expression “x<<k” produces the value $\text{x}{\text{* }}_{\text{w}}^{\text{u}}{\text{2}}^{\text{k}}$

Example:

The example for unsigned multiplication by a power of “2’ is shown below:

Consider an expression $\text{(a<<1)}\text{+}a$. The given expression produces result as “$\text{3 * a}$”.

That is

$\begin{array}{c}\text{(a<<1)}\text{+}\text{a}\text{=}{\text{a*2}}^{\text{1}}\text{+}\text{a}\\ \text{=}\text{a*2}\text{+}\text{a}\\ \text{=}\text{2a}\text{+}\text{a}\\ \text{=}\text{3a}\end{array}$