Octal

related topics
{math, number, function}
{language, word, form}
{area, part, region}
{@card@, make, design}
{work, book, publish}

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 binary digits into groups of three (starting from the right). For example, the binary representation for decimal 74 is 1001010, which can be grouped into (00)1 001 010 — so the octal representation is 112.

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

In octal numerals each place is a power with base 8. For example:

By performing the calculation above in the familiar decimal system we see why 112 in octal is equal to 64+8+2 = 74 in decimal.

Octal is sometimes used in computing instead of hexadecimal.

Contents

Usage

By Native Americans

The Yuki language in California and the Pamean languages[1] in Mexico have octal systems because the speakers count using the spaces between their fingers rather than the fingers themselves[2].

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 the base. In 1718 Swedenborg wrote a manuscript, which has not been published: "En ny räknekonst som omväxlas vid talet 8 istället för det vanliga vid talet 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.[3]

Full article ▸

related documents
Riesz representation theorem
Gram–Schmidt process
Closure (topology)
Linear search
Procedural programming
Arity
Depth-first search
Open set
Recursive descent parser
Compactification (mathematics)
Augmented Backus–Naur Form
Constructible number
Union (set theory)
Hyperbolic function
Legendre polynomials
Decimal
Commutator subgroup
Fixed point combinator
Multiplicative function
Paracompact space
Compactness theorem
Prim's algorithm
Jules Richard
Existential quantification
Integral domain
Rank (linear algebra)
Bolzano–Weierstrass theorem
Pauli matrices
Riemann mapping theorem
Compact space