Binary substraction : 2's complement & carry

Question

I want to substract 1 to the number in binary representation 1010 1101. I write the two s complement of 1: 1111 1111, and I sum with the first number:

bitwise addition, with carry, gives 1 1010 1100: because of carry, I end up with 1 bit more. how is this dealt with in binary addition?

also, I am right in the use of two's complement to do addition?

thanks.

Answer 1

That is an entirely valid and common way to do subtraction, but the 'carry' flag doesn't mean the same thing that it does for normal addition. Since instead of subtracting n, you're adding a large number, the carry flag needs to be handled differently. That extra 1 would usually signify a carry in bitwise addition, whereas here it signifies that everything worked out right. If there wasn't a carry there, it actually means that the result should have been negative - a - b was converted to a + 2^n - b which was less than 2^n, meaning that b > a and so a - b < 0. Either way, it doesn't matter as your result will show up correctly within the 8 bits of your result.