Ad
related to: octal conversion table
Search results
Results From The WOW.Com Content Network
To convert integer decimals to octal, divide the original number by the largest possible power of 8 and divide the remainders by successively smaller powers of 8 until the power is 1. The octal representation is formed by the quotients, written in the order generated by the algorithm. For example, to convert 125 10 to octal: 125 = 8 2 × 1 + 61
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:
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 ...
Coefficients can be larger than one digit, so an efficient way to convert bases is to convert each digit, then evaluate the polynomial via Horner's method within the target base. Converting each digit is a simple lookup table , removing the need for expensive division or modulus operations; and multiplication by x becomes right-shifting.
Positional systems obtained by grouping binary digits by three (octal numeral system) or four (hexadecimal numeral system) are commonly used. For very large integers, bases 2 32 or 2 64 (grouping binary digits by 32 or 64, the length of the machine word) are used, as, for example, in GMP.
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.. Although the word 'byte' had been coined by the designers of the IBM 7030 Stretch for a group of eight bits, it was not yet well known, and English Electric used the word 'syllable' for what is now called a byte.
Such conversion is available for both advanced calculators and programming languages. For example, the hexadecimal representation of the 24 bits above is 4D616E. 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.
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 ...