subtracting a negative 2's complement

Question

I have two 2's complement signed binary numbers and want to subtraction them (assuming an 8-bit subtractor)

1001 0110

1000 0001

what would be the operation to find the difference and why/whynot is there an overflow

Answer 1

to get the difference between 2 numbers you have to subtract them:
1001 0110b = -106
1000 0001b = -127
so -106 - (-127) = 21

you can also do that in binary:

 1001 0110b
-1000 0001b
     =
 0001 0101b

another method is: a-b = a+(-b), so you have to make the 2's complement of the second number. So 1000 0001b becomes 0111 1111b.

  1001 0110b
 +0111 1111b
      =
1 0001 0101b

the first 1 doesn't count because it's a 8bit number, so the result is also 0001 0101b which is 21 in decimal.