Represented in basis X

Question

Let ABCD represent the digits of the starting number.

The four digit number would be represented in basis $X\in \mathbb{N}$ by :

$$\textrm{ABCD}=X^{3}.A+ X^{2}.B+ X^{1}.C+ X^{0}.D$$

Am I right ?

Thanks a lot.

Answer 1

The common conventions for positional systems is that the least significant digit is the rightmost one. This is shared by the Latin, Arabic and Hebrew scripts, notwithstanding the fact that the writing direction is different.

Thus the best bet is that $ABCD$ in base $X$ represents the number $$ D\cdot X^0+C\cdot X^1+B\cdot X^2+A\cdot X^3 $$

Note that an integral base should be greater than $1$.