CS536 Homework 5 Solution

Question 1:

Question 2:

Question 3:

Part a:

Yes. The expression can be evaluated by the above approach

Part b:

The expression can be evaluated using at least 3 registers:

expression AST pseudo code 
 (a - b) - (c - d) 
      -
    /   \
   -     -
  / \   / \
 a   b c   d

  load a into R0
  load b into R1
  R0 = R0 - R1
  load c into R1
  load d into R2
  R1 = R1 - R2
  R0 = R0 - R1

Part c:

The expression can be evaluated using at least 4 registers:

expression AST pseudo code 
 ((a - b) - (c - d)) - ((e - f) - (g - h)) 
            -
         /     \
        /       \
       /         \
      -           -
    /   \       /   \
   -     -     -     -
  / \   / \   / \   / \
 a   b c   d e   f g   h

  load a into R0
  load b into R1
  R0 = R0 - R1
  load c into R1
  load d into R2
  R1 = R1 - R2
  R0 = R0 - R1
  load e into R1
  load f into R2
  R1 = R1 - R2
  load g into R2
  load h into R3
  R2 = R2 - R3
  R1 = R1 - R2
  R0 = R0 - R1