Adding to unsigned and signed binary integers

Question

I was wondering if someone can explain to me what happens when we add binary numbers.

Say we have 4 bits, 0b1111 and we add 1 to 0b1111. I think the binary encoding should be 0b10000; however, since there are only 4 bits the bits will change to 0b0000.

I was wondering why this happens, is it because there's not enough space? How would we add 1 to it if 0b1111 was a signed integer?

Answer 1

if 0b1111 is an unsigned 4 bit value, with 4 bit storage, it has a value of 15. Adding 1 to it, will give you 16, which cannot be stored in 4 bits. The bits roll over and 0b0000 is stored, giving you a result of 0.

Now, if 0b1111 is a signed 4 bit value, with 4 bit storage. it is generally stored in the two's complement representation. It has a range of -8 to +7. 0b1111 will give you -1. (See here on how to convert.) Adding one to that gives you 0.