ENS = Existing Number System
ANS = Alternate Number System
Several people have asked me to describe an easy way to convert between
integers in ENS and ANS. I will try to explain the procedure I use using
base ten, however the procedure works equally well with other bases>1.
Remember that in base ten, ENS digits are : 0,1,2,3,4,5,6,7,8,9
ANS digits are : 1,2,3,4,5,6,7,8,9,A
where "A" represents the digit ten.
So the only difference between ENS and ANS, is that ENS has the digit 0, and
ANS has the digit A (ten).
Given a number in ENS, start at the leftmost digit, and locate the first
zero digit. Borrow one from the digit to its immediate left, and change the
zero digit to A. Carry on this process until the number has no more zero
digits left.
The reverse procedure is:
Given a number in ANS, start again at the leftmost digit, and locate the
first ten digit (A). Add one to the digit to its immediate left, and change
the A digit to zero. Carry on this process until the number has no more
A digits left.
Examples:
Converting ENS to ANS Converting ANS to ENS
ENS = 1240301 ANS = 123A2A1
= 123A2A1 = ANS = 1240301 = ENS
ENS = 20030 ANS = 19A2A
= 1A02A = 1A030
= 19A2A = ANS = 20030 = ENS
ENS = 2000 ANS = 199A
= 1A00 = 19A0
= 19A0 = 1A00
= 199A = ANS = 2000 = ENS
ENS = 1010 ANS = 9AA
= A0A = A0A
= 9AA = ANS = 1010 = ENS
ENS = 10000 ANS = 999A
= A000 = 99A0
= 9A00 = 9A00
= 99A0 = A000
= 999A = ANS = 10000 = ENS
ENS = 1001001 ANS = 99A9A1
= A00A01 = 9A0A01
= 9A09A1 = A01001
= 99A9A1 = ANS = 1001001 = ENS
ENS = 10110110 ANS = 9AA9AAA
= A10A10A = A0AA0AA
= A0AA0AA = 1010A10A
= 9AA9AAA = ANS = 10110110 = ENS
Practice more on your own, and soon you will easily be able to convert any
numbers from ENS to ANS and back.
Enjoy.