Multipurpose Algorithm

The number to be subtracted is negated by the usual means (reflect the bits, add one):

0001 1011 →  1110 0101

Then the "binary addition algorithm" is used:

11100 001
 0011 0001    =  4910
 1110 0101    = -2710
 ---------     -----
 0001 0110       2210

Since the carry into the most significant column is the same as the carry out of that column, the result is correct. We are getting quite a bit of use out of the "binary addition algorithm". It is used to:

• Add integers represented in unsigned binary.
• Add integers represented in two's complement binary.
• Subtract integers represented in two's complement binary.

It can't be used directly to subtract integers represented in unsigned binary. (If both unsigned integers are small enough, the one being subtracted can be represented as a two's complement negative, and then the algorithm can be used.) In the programming language Java all integers (int and long) are represented using two's complement.