binary - Which arithmetic operations are the same on unsigned and two's complement signed numbers?

Question

I'm designing a simple toy instruction set and accompanying emulator, and I'm trying to figure out what instructions to support. In the way of arithmetic, I currently have unsigned add, subtract, multiply, and divide. However, I can't seem to find a definitive answer to the following question: Which of the arithmetic operators need signed versions, and for which are the unsigned and two's complement signed versions equivalent?

So, for example, 1111 in two's complement is equal to -1. If you add 1 to it and pretend that it's an unsigned number , you get 0000, which is correct even when thinking of it as -1. However, does that hold for all numbers? And what about for the other three operations (subtraction, multiplication, division)?

Answer 1

Add and subtract are the same for signed and unsigned 2s complement, assuming you're going to handle overflow/underflow in the normal way for most CPUs, i.e. just wrap around. Multiply and divide are different. So you only need one addition routine and one subtraction routine regardless of signedness, but you need separate signed and unsigned multiply and divide.