Alternative decimal number representation

Question

In class we had an overview of different representations of numbers. Some examples were: decimal, roman numerals, binary, Redundant binary representation, church numerals...

Then the teacher gave an example of representing some numbers differently in the decimal system: $$\begin{matrix} & 0 & 0 & 0 & 0 & 0\\ - & 0 & 0 & 0 & 0 & 1\\ \hline \ldots & 9 & 9 & 9 & 9 & 9 \end{matrix}$$

It's similar to the concept that $0.999\ldots = 1$.

Is there a name to this idea. I would like to read some more about that. But I don't know what to search for.

Thanks in advance!

Answer 1

If the $\ldots$ means that you go on to infinity on the left, then it's called the 10-adic representation (see https://en.wikipedia.org/wiki/P-adic_number).

If you truncate to a fixed finite number of digits (say $n$) you call it an $n$ digit 10s complement representation. (Google will find you lots of links.)

Answer 2

This method of writing negative numbers is known as 2's complement when using base 2, so would most likely be called 10's complement in base 10. Computers use this format, usually having the most significant bit being the 'sign' of the number, where 0 is positive and 1 is negative. This allows computers to add positive and negative numbers with a simple ripple-carry binary adder, allowing subtraction to be done without the need for an extra circuit. To negate a number using 2's complement, simply invert all of the bits, and add 1.