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"A base is a natural number B whose powers (B multiplied by itself some number of times) are specially designated within a numerical system." [1]: 38 The term is not equivalent to radix, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers. [1]
The same sequence of symbols may represent different numbers in different numeral systems. For example, "11" represents the number eleven in the decimal or base-10 numeral system (today, the most common system globally), the number three in the binary or base-2 numeral system (used in modern computers), and the number two in the unary numeral ...
Each of these number systems is a positional system, but while decimal weights are powers of 10, the octal weights are powers of 8 and the hexadecimal weights are powers of 16. To convert from hexadecimal or octal to decimal, for each digit one multiplies the value of the digit by the value of its position and then adds the results. For example:
The duodecimal system, also known as base twelve or dozenal, is a positional numeral system using twelve as its base.In duodecimal, the number twelve is denoted "10", meaning 1 twelve and 0 units; in the decimal system, this number is instead written as "12" meaning 1 ten and 2 units, and the string "10" means ten.
If we use the entire collection of our alphanumerics we could ultimately serve a base-62 numeral system, but we remove two digits, uppercase "I" and uppercase "O", to reduce confusion with digits "1" and "0". [15] We are left with a base-60, or sexagesimal numeral system utilizing 60 of the 62 standard alphanumerics. (But see Sexagesimal system ...
A ternary / ˈ t ɜːr n ər i / numeral system (also called base 3 or trinary [1]) has three as its base.Analogous to a bit, a ternary digit is a trit (trinary digit).One trit is equivalent to log 2 3 (about 1.58496) bits of information.
Octal numeral system (base 8) Nonary (novenary) numeral system (base 9) Decimal (denary) numeral system (base 10) Bi-quinary coded decimal – Numeral encoding scheme; Negative base numeral system (base −10) Duodecimal (dozenal) numeral system (base 12) Hexadecimal numeral system (base 16) Vigesimal numeral system (base 20) Sexagesimal ...
As with the octal and hexadecimal numeral systems, quaternary has a special relation to the binary numeral system.Each radix four, eight, and sixteen is a power of two, so the conversion to and from binary is implemented by matching each digit with two, three, or four binary digits, or bits.