In general binary operation that 11111111(255)+00000001(1)=100000000(256)
The operation result will be 0 for 8 bit Adder, because the processor is 8 bits only.
If a processor support saturated arithmetic, 255+1 would be 255 (stop at max or min value), and it would not overflow or underflow.
Reference:
http://www.techbang.com/posts/10678-fully-understand-arm-processors-cisc-and-risc-are-what-history-structure-a-see-through-the-computer-96-issues-cover-story-the-king?page=2
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