Complementary Subtraction

1-22 Step 4—Remember to discard any carry beyond the size of the original number. Our original problem had four digits, so we discard the carry that expanded the difference to five digits. This carry we disregard is significant to the computer. It indicates that the difference is positive. Because we have a carry, we can read the difference directly without any further computations. Let's check our answer: If we do not have a carry, it indicates the difference is a negative number. In that case, the difference must be R's complemented to produce the correct answer. Let's look at an example that will explain this for you. Subtract 9₁₀ from 5₁₀ (1001₂ from 0101₂): Step 1—Leave the minuend alone: 0101₂ remains 0101₂ Step 2—R's complement the subtrahend: 0111₂ R's complement of subtrahend Step 3—Add the R's complement found in step 2 to the minuend of the original problem: Step 4—We do not have a carry; and this tells us, and any computer, that our difference (answer) is negative. With no carry, we must R's complement the difference in step 3. We will then have arrived at the answer (difference) to our original problem. Let's do this R's complement step and then check our answer: 0100₂ R's complement of difference in step 3 Remember, we had no carry in step 3. That showed us our answer was going to be negative. Make sure you indicate the difference is negative. Let's check the answer to our problem: