| From the Latin term “octo,” meaning eight; an octal is a number system that uses eight single-digit numbers: 0 through 7. There are no 8s or 9s. In this base-8 number system, the number sequence goes like this: 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14,
15, 16, 17, 20, 21, and so on.
Base-8, or octal, counting probably seems awkward to most people because the base-10 is so common. We all know the base-10 system, which emerged centuries ago simply because humans had 10 fingers and thumbs to use for counting. Unfortunately, base-10 isn’t
useful to mathematicians because it has only two divisors, and 10 is not a prime number. Several European mathematicians tried to replace the decimal system during the 18th and 19th centuries. The mathematicians didn’t succeed, but they did try binary
(base 2), octal (base 8), and hexadecimal (base 16) systems.
The octal system, although not popular for mathematical purposes, became useful in 20th-century computer science. Programmers use it as a shorthand approach to represent binary numbers. Binary numbers use six-bit characters. With the octal system, each three
bits is converted into one octal digit, saving considerable diskette or hard drive space. |
