Two's complement is a method of representing signed integers in binary. Here is an explanation of how addition works with two's complement numbers:

• In two's complement, the most significant bit indicates the sign of the number. 0 is positive, 1 is negative.
• To add two two's complement numbers, you can simply add the binary digits as if they were unsigned integers.
• The catch is if there is an overflow past the most significant bit, the result needs to wrap around to fit back into the available bits.

For example, let's add 5 and -3 in 8-bit two's complement:

5: 0000 0101 -3: 1111 1101

Adding them normally: 0000 0101 1111 1101

0001 0010

But this doesn't fit in 8 bits. To wrap the result, we discard the leftmost bit, leaving 0010. This wraps the result to -6, which is correct when adding 5 + -3.

So in summary, two's complement addition works by:

1. Adding normally as if unsigned
2. Wrapping if overflow past the MSB This allows simple circuitry to add both positive and negative numbers.