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The binary digits are grouped by threes, starting from the least significant bit and proceeding to the left and to the right. Add leading zeroes (or trailing zeroes to the right of decimal point) to fill out the last group of three if necessary. Then replace each trio with the equivalent octal digit. For instance, convert binary 1010111100 to ...
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.
Computer engineers often need to write out binary quantities, but in practice writing out a binary number such as 1001001101010001 is tedious and prone to errors. Therefore, binary quantities are written in a base-8, or "octal", or, much more commonly, a base-16, "hexadecimal" ( hex ), number format.
In general, the number of possible values that can be represented by a digit number in base is . The common numeral systems in computer science are binary (radix 2), octal (radix 8), and hexadecimal (radix 16). In binary only digits "0" and "1" are in the numerals.
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 ...
Hexadecimal to octal transformation is useful to convert between binary and Base64. 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 ...
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In a fixed-width binary code, each letter, digit, or other character is represented by a bit string of the same length; that bit string, interpreted as a binary number, is usually displayed in code tables in octal, decimal or hexadecimal notation. There are many character sets and many character encodings for them.