# Dictionary Definition

octal adj : of or pertaining to a number system
having 8 as its base; "an octal digit"

# User Contributed Dictionary

## English

### Noun

octal (uncountable)- The number system that uses the eight digits 0, 1, 2, 3, 4, 5, 6, 7.

- arithmetic computing Concerning numbers expressed in octal or mathematical calculations performed using octal.

#### Synonyms

- base-8

### See also

# Extensive Definition

The octal numeral
system, or oct for short, is the base-8 number system, and uses the
digits 0 to 7. Numerals can be made from binary
numerals by grouping consecutive digits into groups of three
(starting from the right). For example, the binary representation
for decimal 74 is 1001010, which groups into 001 001 010
— so the octal representation is 112.

In decimal systems each decimal place is a base
of 10. For example:

- \mathbf = \mathbf \times 10^1 + \mathbf \times 10^0

- \mathbf = \mathbf \times 8^2 + \mathbf \times 8^1 + \mathbf \times 8^0

Octal is sometimes used in computing instead of hexadecimal.

## Usage

### By Native Americans

The Yuki language in California and the Pamean languages in Mexico have octal systems because the speakers count using the spaces between their fingers rather than the fingers themselves.### In Europe

In 1716 King Charles
XII of Sweden asked Emanuel
Swedenborg to elaborate a number system based on 64 instead of
10. Swedenborg however argued that for people with less
intelligence than the king such a big base would be too difficult
and instead proposed 8 as base. In 1718 Swedenborg wrote a
manuscript, which has not been published: "En ny rekenkonst som om
vexlas wid Thalet 8 i stelle then wanliga wid Thalet 10" ("A new
arithmetic (or art of counting) which changes at the Number 8
instead of the usual at the Number 10"). The numbers 1-7 are there
denoted by the consonants l, s, n, m, t, f, u (v) and zero by the
vowel o. Thus 8 = "lo", 16 = "so", 24 = "no", 64 = "loo", 512 =
"looo" etc. Numbers with consecutive consonants are pronounced with
vowel sounds between in accordance with a special rule.

### In fiction

- The fictional alien felinoid species Kilrathi of the Wing Commander universe count in octal, since their paws have 4 toes instead of 5.
- The Octospider species of Rendezvous with Rama and the computer game RAMA use a colour code based on octal system, and its comprehension is a puzzle of the game scenario.
- The Alterans from Stargate SG-1 used octal, even though they had ten fingers. It's possible that they counted the gaps between each finger, ignored the thumb on each hand, or used the thumb as a base-2 counter (as on an abacus) allowing them to count up to 30 (24 in decimal) on their hands.
- The satirist Tom Lehrer famously remarked in his song parodying new math that "base 8 is just like base 10... if you're missing two fingers."
- In the first-person shooter Prey, numerical codes to open doors are entered in octal.
- The Tau race in the Warhammer 40,000 universe use the octal system.
- In The Beekeeper's Apprentice, Laurie R. King's first Sherlock Holmes pastiche featuring Mary Russell, base eight math played a key role in solving the mystery.

### In computers

Octal is sometimes used in computing instead of hexadecimal, perhaps most often in modern times in conjunction with file permissions under Unix systems (see chmod). It has the advantage of not requiring any extra symbols as digits (the hexadecimal system is base-16 and therefore needs six additional symbols beyond 0–9). It is also used for digital displays.At the time when octal originally became widely
used in computing, systems such as the IBM
mainframes employed 24-bit (or 36-bit) words. Octal was an
ideal abbreviation of binary for these machines because eight (or
twelve) digits could concisely display an entire machine word (each
octal digit covering three binary digits). It also cut costs by
allowing Nixie tubes,
seven-segment
displays, and calculators to be used for
the operator consoles; where binary displays were too complex to
use, decimal displays needed complex hardware to convert radixes,
and hexadecimal displays needed to display letters.

All modern computing platforms, however, use 16-,
32-, or 64-bit words, with eight bits making up a byte. On such
systems three octal digits would be required, with the most
significant octal digit inelegantly representing only two binary
digits (and in a series the same octal digit would represent one
binary digit from the next byte). Hence hexadecimal is more
commonly used in programming languages today, since a hexadecimal
digit covers four binary digits and all modern computing platforms
have machine words that are evenly divisible by four.

The prefix customarily used to represent an octal
number is "o" (i.e. o73), as binary and hexadecimal are represented
by 'b' and 'h' respectively.

## Conversion between bases

For more information and other bases, see Conversion among bases.### Decimal – Octal Conversion

#### Method of consecutive divisions by 8

Is used to convert integer decimals to octals and consists in dividing the original number by the largest possible factor of 8 and successively dividing the remainders by successively smaller factors of 8 until the factor is 0. The octal number is formed by the quotients, written in the order of its obtention. for example convert the following to octal 75.8 solution:- 125/8^2=1 125-((8^2)*1)=61 61/8^1=7 61-((8^1)*7)=5 125(base10)=175(base8)900/8^3=1

900-((8^3)*1)=388

388/8^2=6

388-((8^2)*6)=4

4/8^1=0

4-((8^1)*0)=4

4/8^0=4

900(base10)=1604(base8)

#### Method of consecutive multiplications by 8

Is used to convert a decimal fraction to octal. The decimal fraction is multiplied by 8, and the integer part of the result is the first digit of the octal fraction. The process is repeated with the fractionary part of the result, until it is null or within acceptable error parameter. Example: Convert 0.140625 to octal: 0.140625 x 8 = 1.125 0.125 x 8 = 1.0Previous methods can be combined to convert
decimal numbers with integer and fractionary parts.

If you want to convert decima number to other
number system as hexadecimal, octal, binary etc. You must divide
the number by the number system you converting to. For example
decimal to hexadecimal:610

3050/16 = 190 rem 10 190/16 = 11 rem 14 11/16 = 0
rem 11 asw: BEA

remember when you write your answer you start
from bottom to the top.

### Octal – Decimal Conversion

Use the formula:- \sum_^n \left( a_i\times B^i \right).

Example: Convert octal 764 to decimal system. 764
(base 8) = 7 x 8² + 6 x 8¹ + 4 x 8° = 448 + 48 + 4 = 500 (base
10)

For double digit numbers this method amounts to
taking the first number, multiplying it by 8 and then adding the
second to get the total. Example: 65 in octal would be 53 in
decimal (6*8 + 5 = 53)

### Octal – Binary Conversion

To convert octals to binaries, replace each digit of octal number by its binary correspondent. Example: Convert octal 1572 to binary. 1 5 7 2 = 001 101 111 010### Binary – Octal Conversion

The process is the reverse of previous algorithm. The binary digits are grouped 3 by 3, from the decimal point to the left and to the right. Then each trio is substituted by the equivalent octal digit.For instance, conversion of binary 1010111100 to
octal:

Thus 10101111002 = 12748

### Octal – Hexadecimal Conversion

The conversion is made in two steps using binary as an auxiliary base. Octal is converted to binary and then to hexadecimal, grouping digits 4 by 4, which correspond each to an hexadecimal digit.For instance, convert octal 1057 to
hexadecimal:

- To binary:

- To hexadecimal:

Thus 10578 = 22F16

### Hexadecimal – Octal Conversion

Reverse the previous algorithm.## See also

- Computer numbering formats
- Octet, a grouping of eight bits

## References

## External links

- Online Converter for Decimal/Octal Numerals (JavaScript, GPL)
- Online tool to convert ASCII text to Octal numbers
- Octomatics is a numeral system enabling simple visual calculation in octal.

octal in Catalan: Sistema octal

octal in Czech: Osmičková soustava

octal in Danish: Oktale talsystem

octal in German: Oktalsystem

octal in Modern Greek (1453-): Οκταδικό σύστημα
αρίθμησης

octal in Spanish: Sistema octal

octal in Esperanto: Okuma sistemo

octal in Basque: Zenbaki-sistema zortzitar

octal in French: Système octal

octal in Galician: Código octal

octal in Korean: 팔진법

octal in Indonesian: Oktal

octal in Icelandic: Áttundakerfi

octal in Italian: Sistema numerico ottale

octal in Hebrew: בסיס אוקטלי

octal in Haitian: Sistèm oktal

octal in Hungarian: Nyolcas számrendszer

octal in Dutch: Octaal

octal in Japanese: 八進法

octal in Norwegian: Åttetallsystemet

octal in Norwegian Nynorsk:
Åttetalssystemet

octal in Polish: Ósemkowy system liczbowy

octal in Portuguese: Sistema octal

octal in Russian: Восьмеричная система
счисления

octal in Serbian: Октални систем

octal in Finnish: Oktaalijärjestelmä

octal in Swedish: Oktala talsystemet

octal in Tamil: எண்ணெண்

octal in Thai: เลขฐานแปด

octal in Vietnamese: Hệ bát phân

octal in Chinese: 八进制