What happens exactly when adding or subtracting two's complement numbers outside the range of representation?

Question

If there is 11 bit two's complement number with a range of -1024 to 1023, what happens if we go outside that range? For example, I have -1024 and I subtract 1. Or I have 1023 and I add 1. Does it crash? Stay unchanged? Change to different number?

Answer 1

-1025 cannot be represented by an 11-bit two’s complement number. If we add them, there's an overflow:

-1024 =   10000000000 => 11 bits
-1 =     +11111111111 => 11 bits
         ------------
         101111111111 => 12 bits

What happens next depends on your implementation. As this is a question of fixed-width binary numbers, we drop the overflow bit, leaving us with 01111111111 or 1023.

There are many similar questions on Stack Overflow that you may want to look at.