Octal
Octal system (also known as base 8 or octonary), is a numeral system that uses the numerals 0 through 7. The system is similar to binary (base 2) and hexadecimal (base 16). Octal numerals are written using the number 0 before the numeral, for example, 004 or 01242. Octal numbers are also sometimes written with a small 8 to the lower right, as in 12428.
At one time, the octal system was used mainly for work with computers. It provided an easier way to work with binary numbers. As computers changed from using 24-bit systems to 32- and 64-bit systems, hexadecimal replaced octal for most uses. Certain groups, for example, Native Americans using the Yuki language in California and the Pamean languages[1] in Mexico, also use an octal numbering system. They do this because when they count, they use the spaces between their fingers instead of counting the actual fingers.
Octal system
the octal system has no letters of the alphabet
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Octal and decimal
In the decimal system (base 10), each digit in octal is equal to that digit multiplied by the exponent of 8 that is equal to its location minus one.
Location | ||||||
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6 | 5 | 4 | 3 | 2 | 1 | |
Value | 32768 (85) | 4096 (84) | 512 (83) | 64 (82) | 8(81) | 1 (80) |
Example: o3425 to decimal
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Octal and hexadecimal
Octal is similar to hexadecimal because they are both easily converted to binary. Where octal is equal to three-digit binary, hexadecimal is equal to four-digit binary. Where octal numerals start with the letter "o", hexadecimal numerals end with the letter "h". The easiest way to convert from one to the other is to convert to binary and then to the other system.
Octal | Binary | Hexadecimal | ||||||||
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three digit | four digit | |||||||||
o4 | 100 | 0100 | 04h | |||||||
o15 | 001 | 101 | 1101 | 0Dh | ||||||
o306 | 011 | 000 | 110 | 1100 | 0110 | C6h | ||||
o54253 | 101 | 100 | 010 | 101 | 011 | 0101 | 1000 | 1010 | 1011 | 58ABh |
Octal Media
Fuxi's "Earlier Heaven" Arrangement of the Eight Trigrams
Related pages
References
- ↑ Avelino, Heriberto (2006), "The typology of Pame number systems and the limits of Mesoamerica as a linguistic area" (PDF), Linguistic Typology, 10: 41–60, doi:10.1515/LINGTY.2006.002, S2CID 20412558
Other websites
- Online Converter Archived 2007-01-04 at the Wayback Machine for Decimal/Octal Numerals (JavaScript, GPL)