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Can someone explain why the carry flag does not set when I call inc al in the following code:

mov al,ff 
inc al
int 3

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As far as I understand it moving the hex value ff(255) to the 8-bit register and then incrementing it by one would cause the carry flag to be set because it goes over the maximum value the register can hold. But when I run the code the value in the al register goes back to zero and the carry flag is not set. Can someone explain this better to me?

Zer0F8th
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