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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.
Each hexadecimal digit corresponds to a pair of quaternary digits, and each quaternary digit corresponds to a pair of binary digits. In the above example 2 5 C 16 = 02 11 30 4. The octal (base 8) system can also be converted with relative ease, although not quite as trivially as with bases 2 and 4. Each octal digit corresponds to three binary ...
Octal ( base 8) is a numeral system with eight as the base . In the decimal system, each place is a power of ten. For example: In the octal system, each place is a power of eight. For example: By performing the calculation above in the familiar decimal system, we see why 112 in octal is equal to in decimal.
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". An example and comparison of numbers in different bases is described in the chart below.
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.
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 ...
A binary coderepresents text, computer processor instructions, or any other datausing a two-symbol system. The two-symbol system used is often "0" and "1" from the binary number system. The binary code assigns a pattern of binary digits, also known as bits, to each character, instruction, etc. For example, a binary stringof eight bits (which is ...
Octets can be represented using number systems of varying bases such as the hexadecimal, decimal, or octal number systems. The binary value of all eight bits set (or activated) is 11111111 2, equal to the hexadecimal value FF 16, the decimal value 255 10, and the octal value 377 8. One octet can be used to represent decimal values ranging from ...