Checking Binary Addition

Once you have worked out an 8-bit binary addition, you can check it by converting the two numbers and your answer into denary. As long as the exact total is 255 or less, the two denary values should add up to the denary value of your answer. If they do, the binary result is correct.

A worked check

Suppose you add 0110 and 0011 and your column working gives 1001. To check it:

• 0110 is 6 in denary.
• 0011 is 3 in denary.
• 6 + 3 = 9.
• Your answer, 1001, is 8 + 1 = 9.

Both sides give 9, so the answer fits. If you had written 1000 instead, that is 8, and the check would compare 9 with 8 and fail. The slip is usually a carry missed from the next column, including the final carry into the most significant bit, so go back through the columns rather than changing the answer to fit. The same method works for 8-bit numbers: convert both inputs and your answer to denary and check that the sum of the inputs equals the denary value of your answer, provided the sum is no more than 255.

The check is not the working

Converting and adding in denary only ever confirms a result. It never shows column addition: no carries appear above or below the digits and no column is worked through, so it cannot earn the mark for showing your method. Adding the two denary values and converting the total back into binary may land on the right answer, but it is not accepted as working.

When the denary total is too big

Eight bits can store denary values from 0 to 255 only. If your two denary values add up to more than 255, the exact total needs a ninth bit, so your 8-bit answer will not match the denary total. That is an overflow, not a slip in your columns: give the 8-bit result and state that an overflow has occurred.