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To convert a number k to decimal, use the formula that defines its base-8 representation: = = In this formula, a i is an individual octal digit being converted, where i is the position of the digit (counting from 0 for the right-most digit). Example: Convert 764 8 to decimal:
When converting from binary to octal every 3 bits relate to one and only one octal digit. Hexadecimal, decimal, octal, and a wide variety of other bases have been used for binary-to-text encoding, implementations of arbitrary-precision arithmetic, and other applications. For a list of bases and their applications, see list of numeral systems.
Binary is also easily converted to the octal numeral system, since octal uses a radix of 8, which is a power of two (namely, 2 3, so it takes exactly three binary digits to represent an octal digit). The correspondence between octal and binary numerals is the same as for the first eight digits of hexadecimal in the table above. Binary 000 is ...
That is, the value of an octal "10" is the same as a decimal "8", an octal "20" is a decimal "16", and so on. In a hexadecimal system, there are 16 digits, 0 through 9 followed, by convention, with A through F. That is, a hexadecimal "10" is the same as a decimal "16" and a hexadecimal "20" is the same as a decimal "32".
The prefixes are given from the least significant decimal digit up: units, then tens, then hundreds, then thousands. For example: 548 → octa- (8) + tetraconta- (40) + pentacta- (500) = octatetracontapentacta-
The format is written with an implicit lead bit with value 1 unless the exponent is all zeros. Thus only 236 bits of the significand appear in the memory format, but the total precision is 237 bits (approximately 71 decimal digits: log 10 (2 237) ≈ 71.344). The bits are laid out as follows:
The octal and hexadecimal systems are often used in computing because of their ease as shorthand for binary. Every hexadecimal digit corresponds to a sequence of four binary digits, since sixteen is the fourth power of two; for example, hexadecimal 78 16 is binary 111 1000 2. Similarly, every octal digit corresponds to a unique sequence of ...
The octal representation is 23260556. Those 8 octal digits can be split into pairs ( 23 26 05 56 ), and each pair is converted to decimal to yield 19 22 05 46 . Using those four decimal numbers as indices for the Base64 alphabet, the corresponding ASCII characters are TWFu .