Signed Subtraction Flags Cheat Sheet

signed-cmp.md

Flags table for the operation: a - b

Flag Legend

• Z- Is the result zero?
• S- Is the top bit of the result set?
• C- Did a borrow not occur (see Subtraction on the 6502)?
  • For architectures with a true borrow flag, invert the C bit.
• V- Does the result of a - b fit within signed 16-bit range?

Other notes

• a and b are treated as 16-bit signed numbers.
• -x is unary negation.
• Entries in columns Z, S, C, and V are boolean expressions that evaluate to the value of each flag.

Flags Table

Condition	Z	S	C	V
a > 0, b > 0, a >= b	a == b	0	1	0
a > 0, b > 0, a < b	0	1	0	0
a > 0, b < 0 (a > b)	0	a + -b > 32767	0	a + -b > 32767
a < 0, b > 0 (a < b)	0	a - b >= -32768	1	a - b < -32768
a < 0, b < 0, a >= b	a == b	0	1	0
a < 0, b < 0, a < b	0	1	0	0

Conclusions

• If a >= b, then S and V will have the same value (S xnor V, or S == V).
• If a < b, then S and V will have opposite values (S xor V).
• By using only the first table entry, you can derive flags for unsigned compares too!
  • If a >= b, then C == 1.
  • If a < b, then C == 0.