In November 1994, I developed a positional number system that I called the Alternate Number System (ANS for short). Shortly after its publication in December 1995, I was informed that the system had already been studied by authors such as Salomaa with respect to formal languages. In addition, the system was also published in 1947 by Foster. However, I feel that my approach is a simplified view that can be understood at a much more elementary level. So these pages examine ANS from a simplistic viewpoint. ANS is a system that is more logical than the Existing Number System (ENS for short). I say this because of the following three flaws in ENS.
(1) In ENS, the digit zero behaves differently from other digits. For example, when any two digits (except zero) are added in ENS, the result differs from the original two numbers. When zero, on the other hand, is added to any number, the result is the original number - nothing happens.
(2) In ENS, base 1 is invalid.
(3) In ENS, multidigit numbers such as 12300 "lose" digits when
the digits are reversed and become 321 in the example.
Welcome to ANS in which the digit zero disappears and therefore all digits behave the same. So digit reversals work for all numbers. And, yes, base 1 is valid in ANS.
If you would like to read further, the article is titled
"A Logical Alternative to the Existing Positional Number System"
and was published in Volume 1 (Dec 1995) of the electronic
journal : SouthWest Journal of Pure and Applied Mathematics (swjpam).
However, the journal is no longer in service. So I have supplied a
text version of the original article which can be found at:
text version here.
Enjoy.