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Bailey–Borwein–Plouffe formula. The Bailey–Borwein–Plouffe formula ( BBP formula) is a formula for π. It was discovered in 1995 by Simon Plouffe and is named after the authors of the article in which it was published, David H. Bailey, Peter Borwein, and Plouffe. [ 1] Before that, it had been published by Plouffe on his own site. [ 2]
A senary ( / ˈsiːnəri, ˈsɛnəri /) numeral system (also known as base-6, heximal, or seximal) has six as its base. It has been adopted independently by a small number of cultures. Like the decimal base 10, the base is a semiprime, though it is unique as the product of the only two consecutive numbers that are both prime (2 and 3).
A binary number is a number expressed in the base -2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" ( zero) and "1" ( one ). A binary number may also refer to a rational number that has a finite representation in the binary numeral system, that is, the ...
The most common variants are decimal (base 10) and binary (base 2). The latter is commonly known also as binary scaling. Thus, if n fraction digits are stored, the value will always be an integer multiple of b −n. Fixed-point representation can also be used to omit the low-order digits of integer values, e.g. when representing large dollar ...
Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system ). More generally, a positional system is a numeral system in which the contribution of a digit to the value of a number is the value of the digit multiplied by a factor ...
A non-integer representation uses non- integer numbers as the radix, or base, of a positional numeral system. For a non-integer radix β > 1, the value of. is. The numbers di are non-negative integers less than β. This is also known as a β-expansion, a notion introduced by Rényi (1957) and first studied in detail by Parry (1960).
A negative base (or negative radix) may be used to construct a non-standard positional numeral system. Like other place-value systems, each position holds multiples of the appropriate power of the system's base; but that base is negative—that is to say, the base b is equal to −r for some natural number r ( r ≥ 2 ).
Calculations were performed in base 2 (binary), then the result was converted to base 10 (decimal). The calculation, conversion, and verification steps took a total of 131 days. [41] In August 2010, Shigeru Kondo used Alexander Yee's y-cruncher to calculate 5 trillion digits of π.