ALU Flags

Different CPUs have different things, including flags.

But for a MIP, we have 4:

• Overflow
• Result is zero
• Result is negative

Overflow

• For unsigned numbers, if $C_{out}=1$, then there is overflow
• For signed numbers (either A or B are negative):
  • For G = A + B, we have overflow when
    1. A and B have the same sign
    2. G has opposite sign
  • For G = A - B, we have overflow when
    1. A and B have different signs
    2. G has the same sign as B
    • E.g: A = -2 and B = 15. A - B = -17. B is negative; -17 is negative. We have overflow!
  • For G = A + B and A, B have different signs
    • It can never overflow!

Zero Flag (not on the slides)

$Z={\bar{G}}_3{\bar{G}}_2{\bar{G}}_1{\bar{G}}_0$ =$\overline{G_3+G_2+G_1+G_0}$

• Checks if any number is 1. If it is, it’s not zero!