Question

So I was practicing my binary subtraction. It’s been a long while since my first exam and I decided to create my own tricky binary subtraction and I came up with this one:

 1100
-1101

Of course the “borrowing trick” does not work for this problem at least I could not get it to work. Is my only choice to flip the bits of the second binary number(the bottom one) and then add a one basically doing 2’s complement so 1101 becomes 0011. Then add the primary binary number(1100) with the 2’s complement representation(0011) which means it would look like this:

    1100 (-4) assume 2's complement
+   0011 (3)  assume 2's complement

sum:1111 (-1) assume 2's complement

I just need confirmation on this problem since its been a long time since I did binary subtraction.

Answer 1

 1100
-1101

0 - 1 = 1 (borrow 1)

 1100
-1101
   1
=====
    1

0 - 0 - 1 = 1 (borrow 1)

 1100
-1101
  11
=====
   11

1 - 1 - 1 = 1 (borrow 1)

 1100
-1101
 111
=====
  111

1 - 1 - 1 = 1 (borrow 1)

 1100
-1101
1111
=====
 1111

The result is 1111 with 1 borrowed. In terms of unsigned arithmetic, this means that either the result underflowed or you need to borrow from the next significant digit. (In terms of signed arithmetic there is no overflow as you have also borrowed the second bit and the calculation corresponds to -4 - -3 = -1.)