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Quaternary numeral system (base 4) Quater-imaginary base (base 2 √ −1) Quinary numeral system (base 5) Pentadic numerals – Runic notation for presenting numbers; Senary numeral system (base 6) Septenary numeral system (base 7) Octal numeral system (base 8) Nonary (novenary) numeral system (base 9) Decimal (denary) numeral system (base 10)
Base Name Usage 2: Dyadic number: 3: Triadic number: 4: Tetradic number: the same as dyadic number 5: Pentadic number: 6: Hexadic number: not a field: 7: Heptadic number: 8: Octadic number: the same as dyadic number 9: Enneadic number: the same as triadic number 10: Decadic number: not a field 11: Hendecadic number: 12: Dodecadic number: not a ...
For example, in the decimal system (base 10), the numeral 4327 means (4×10 3) + (3×10 2) + (2×10 1) + (7×10 0), noting that 10 0 = 1. In general, if b is the base, one writes a number in the numeral system of base b by expressing it in the form a n b n + a n − 1 b n − 1 + a n − 2 b n − 2 + ... + a 0 b 0 and writing the enumerated ...
In books and articles, when using initially the written abbreviations of number bases, the base is not subsequently printed: it is assumed that binary 1111011 is the same as 1111011 2. The base b may also be indicated by the phrase "base-b". So binary numbers are "base-2"; octal numbers are "base-8"; decimal numbers are "base-10"; and so on.
The only base-4 repunit prime is 5 (). = (+) (), and 3 always divides + when n is odd and when n is even. For n greater than 2, both + and are greater than 3, so removing the factor of 3 still leaves two factors greater than 1.
With base e the natural logarithm behaves like the common logarithm in base 10, as ln(1 e) = 0, ln(10 e) = 1, ln(100 e) = 2 and ln(1000 e) = 3 (or more precisely the representation in base e of 3, which is of course a non-terminating number).