Children's Math

I was discussing teaching our young daughter how to subtract large numbers and other children's math methods with my brother and he asked, "How does a microprocessor do it?" (We're both engineers; I'm an integrated circuit designer) My response? "They don't [subtract]. They take the two's complement [of the subtrahend] and then add." I thought this idea might help improve my children's math teaching skills.

Microprocessors work in base 2 (each digit of every number is either 0 or 1), but let's do a subtraction example in base 10 (each digit between 0 and 9 inclusive) the way a microprocessor would subtract if it was a human being. It's really easy, easier than the method we humans commonly use.

230895

- 3904

----------------

996095

1

(1)226991

In the figure above, we start by computing the nine's complement of the subtrahend (the number we're subtracting from the top number). The nine's complement of a number is just the number who's individual digits in each column add up to nine with the digits of the original number.

For this example, the nine's complement of 3904 is 996095. To do the "subtraction" you need to extend the nine's complement to be as wide as the minuend (the top number) so insert leading zeros to make 3904 into 003904 and then for each column write down the digit that with the subtrahend (003904) sums to 9 for that column (you write the digit: 9 minus subtrahendDigit). That's how we get 996095.

To get the answer add the minuend (top number), the nine's complement of the subtrahend and "1". There will always be an overflow (a 1 in the column farther left than the leftmost digit of the minuend); remove that 1 from the answer and you're done! Children's math can be child's play!

Please visit the latest version of this article on our web-site which includes graphics illustrating the example: Children's Math.

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