I am taking an electrical engineering course as part of my computer science degree and we are talking about how a computer performs math computations only using addition. I understand this because multiplication is a series of additions. Subtraction is like adding the negative value. To do subtraction you have to find the two's complement and then perform the addition. I started getting lost when we got into binary math using signed numbers. I think I understand how to perform multiplication using signed numbers - I think you find the two's complement of the negative, multiply, add, find the two's complement of the result and append the sign bit accordingly. Binary division with signed numbers I don't understand well.

For example,

1111 / 0101 

These are signed numbers so the decimal equivalent would be -7 / 5. The answer would be -1R2. If I convert that to signed binary numbers wouldn't that be 1001 0010? So to get there I would have to do 111 - 101 = 010. However, 11 could also be -1, so would I back fill 1s and get 1111 0010? Another question, is about that subtraction - doesn't that need to be changed to addition? If so, wouldn't the problem become 111 + 011 (the twos complement of 010)?

The more I look at it, the more confused I get. Any help would be appreciated.