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The f
register consists of eight (semi)independent bits which give you information about previous instructions' results. Not all instructions set all (or any) bits  see their individual documentation for more information.
1
if the result is negative (in two's complement representation), 0
otherwise. In other words, it's a copy of bit 7 (the high bit) of the result.
1
if the result is zero, 0
otherwise.
Simply a copy of bit 5 of the result, it's not very useful.
Set if there's been a carry between bit 3 and bit 4 of the result. It's used by the daa
instruction and isn't useful for much else.
Simply a copy of bit 3 of the result, it's not very useful.
It's either the parity of the result (1
if there is an even number of 1s in the binary representation of the result, 0
if odd); or it's the two's complement overflow (1
if the operation caused the result to go past the 128/+127 limit, 0
otherwise).
1
if the last daa
compatible instruction was a subtraction, 0
if it was an addition. It's used by the daa
instruction and isn't useful for much else.
1
if there was a carry into or out of the high bit of the result; in other words, if the operation caused the number to go past the 0/255 boundary.