# 9's complement

1. Feb 15, 2009

### snoggerT

Find the 4-digit complement of a) 0232 b) 9644

3. The attempt at a solution

I'm not really sure what is being asked here. When asked what form the numbers were given in and whether the problem was talking about 9's complement, his response was "the answer is 9's complement". So I don't really know what to do since they appear to be in 9's complement form already. Does anyone think they can help?

2. Feb 15, 2009

### mathmate

One of the uses of 9's complement notation is to convert a decimal into its negative form so that an addition can be performed instead of subtraction, thus obviating the necessity of borrowing, etc.

The nine's complement can be obtained by subtracting from nine of each and every digit of the original number.

For example, the nine's complement of 1357 would be 8642, since 9-1=8, 9-3=6, 9-5=4, 9-7=2.

To do a subtraction, we simply add the first number to the nine's complement of the second number, PLUS 1, then ignore the 'Carry'.

For example, to do 524-256
we calculate 524+743+1=1268, drop the 1 (carry) to give 268.

See for example:
http://en.wikipedia.org/wiki/Ten's_complement

3. Feb 15, 2009

### snoggerT

thanks. I just wanted to make sure on that.