Question

Why does the 1's complement subtraction algorithm work?

a. It simplifies the calculation process
b. It ensures numerical stability
c. It avoids overflow issues
d. It corrects rounding errors

Answer 1

The 1's complement subtraction algorithm works by simplifying the calculation process through the use of 1's complement and carry operations.

Step-by-step explanation:

The 1's complement subtraction algorithm works because it simplifies the calculation process by eliminating the need to borrow or carry digits. In this algorithm, to subtract one number from another, we take the 1's complement of the subtrahend (by flipping the bits) and add it to the minuend along with a carry of 1. This eliminates the need for separate addition and subtraction operations, making the calculation faster and easier.

For example, to subtract 5 from 9 using 1's complement subtraction:

1. 1's complement of 5 is 1010.
2. Add 1 to the 1's complement: 1010 + 1 = 1011.
3. Add the minuend (9) to the 1's complement and carry: 9 + 1011 + 1 = 10010.
4. Drop the carry (1) and the first digit (1): 0010.
5. The result is 2, which is the correct answer (9 - 5 = 2).