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June 18, 2011


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Bill St.John

Interesting but...
What if the result is negative?
23-47 = -24 (standard arithmetic)
23+52 = 75 (9s complement addition)

The method falls apart here BUT if we take the result of the 9s complement addition and do a 9s complement again, we get 24.

John Dunn

Hi, Bill.

I don't know how to deal with neagtive results either, it's always been a larger number take away a smaller number for me.

However, this process works in any base including binary for which ones-complment arithmetic is used.

For example: 1011 - 101 = 110 in plain subtrection.
Then: 1011 + 1010 = 10101 --> 0101 + 1 = 110 Correct.


The method is (assuming x and y contain 4 digits):

x - y = x + (10000 - y) = 10000 + (x - y)

Therefore dropping the leading 1 gives you the correct result.

If (x - y) is negative, you just have to take the 9's complement again:

(e.g. 9's complement of 75 is 24)


My previous comment should read:

The method to calculate (x - y) is:

x + (10000 -y) = 10000 + (x - y)

(assuming x and y contain 4 digits)

Note that (10000 - y) us the 10's complement of y, or 9's complement + 1. Dropping the leading 1 gives you the correct result.

If (x - y) is negative, you just have to take the 9's complement again:

10000 - (10000 + (x - y)) = -(x - y)

Just be aware that the result is a negative value
(e.g. 9's complement of 75 is 24, and the actual result is -24)

Hope this clear things up.

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