i have a question about numeral systems that use the place value concept , in the decimal system the position is a power of ten and it has set of ten unique digits, the binary system its position is a power of two and it has a set of two unique digits and so on for all systems that use the place value concept
my question is why the position value depends in the number of digits ? why cant we have a system that has n unique digits and use a position value different than n let's say m for example ?
2026-03-27 00:58:13.1774573093
the logic of numeral systems
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I suggest trying some examples and seeing which number representations you get.
If $n<m$, then some numbers will not be representable (e.g. in base 10 with digits up to 8, you can't represent the number 19). If $n>m$, then some numbers will have multiple representations (e.g. "3" and "11" in base 2). The only way to ensure every number has a unique representation is for the number of digits to match the position value.