Carry Flag, Auxiliary Flag and Overflow Flag in Assembly

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Carry Flag

The rules for turning on the carry flag in binary/integer math are two:

  1. The carry flag is set if the addition of two numbers causes a carry
    out of the most significant (leftmost) bits added.
    1111 + 0001 = 0000 (carry flag is turned on)

  2. The carry (borrow) flag is also set if the subtraction of two numbers
    requires a borrow into the most significant (leftmost) bits subtracted.
    0000 – 0001 = 1111 (carry flag is turned on)
    Otherwise, the carry flag is turned off (zero).

    • 0111 + 0001 = 1000 (carry flag is turned off [zero])
    • 1000 – 0001 = 0111 (carry flag is turned off [zero])

In unsigned arithmetic, watch the carry flag to detect errors.

In signed arithmetic, the carry flag tells you nothing interesting.

Overflow Flag

The rules for turning on the overflow flag in binary/integer math are two:

  1. If the sum of two numbers with the sign bits off yields a result number
    with the sign bit on, the “overflow” flag is turned on.
    0100 + 0100 = 1000 (overflow flag is turned on)

  2. If the sum of two numbers with the sign bits on yields a result number
    with the sign bit off, the “overflow” flag is turned on.
    1000 + 1000 = 0000 (overflow flag is turned on)

Otherwise the “overflow” flag is turned off

  • 0100 + 0001 = 0101 (overflow flag is turned off)
  • 0110 + 1001 = 1111 (overflow flag turned off)
  • 1000 + 0001 = 1001 (overflow flag turned off)
  • 1100 + 1100 = 1000 (overflow flag is turned off)

Note that you only need to look at the sign bits (leftmost) of the three
numbers to decide if the overflow flag is turned on or off.

If you are doing two’s complement (signed) arithmetic, overflow flag on
means the answer is wrong – you added two positive numbers and got a
negative, or you added two negative numbers and got a positive.

If you are doing unsigned arithmetic, the overflow flag means nothing
and should be ignored.

For more clarification please refer: http://teaching.idallen.com/dat2343/10f/notes/040_overflow.txt

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