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The conversion is made in two steps using binary as an intermediate base. Octal is converted to binary and then binary to hexadecimal, grouping digits by fours, which correspond each to a hexadecimal digit. For instance, convert octal 1057 to hexadecimal: To binary:
Each octal digit corresponds to three binary digits, rather than four. Therefore, we can convert between octal and hexadecimal via an intermediate conversion to binary followed by regrouping the binary digits in groups of either three or four.
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:
Syllabic octal and split octal are two similar notations for 8-bit and 16-bit octal numbers, respectively, used in some historical contexts. Syllabic octal [ edit ] Syllabic octal is an 8-bit octal number representation that was used by English Electric in conjunction with their KDF9 machine in the mid-1960s.
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 ...
Octal: Charles XII of Sweden, Unix-like permissions, Squawk codes, DEC PDP-11, Yuki, Pame, compact notation for binary numbers, Xiantian (I Ching, China) 9: Nonary, nonal: Compact notation for ternary: 10: Decimal, denary: Most widely used by contemporary societies [29] [30] [31] 11: Undecimal, unodecimal, undenary
Floating-point formats. In computing, octuple precision is a binary floating-point -based computer number format that occupies 32 bytes (256 bits) in computer memory. This 256- bit octuple precision is for applications requiring results in higher than quadruple precision.
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 ...