Octal, a base-8 number system, is used in various computing applications, serving as a convenient shorthand for representing binary data. This system operates using eight digits: 0 through 7, each digit representing a unique power of 8.
Let’s delve into more examples of octal numbers. If we take the octal number 753, the ‘3’ at the end is in the ones place (8^0), the ‘5’ is in the eights place (8^1), and the ‘7’ is in the sixty-fourths place (8^2). Converting this to a decimal system, we calculate it as (764) + (58) + (3*1), which equals 491.
Octal becomes particularly useful when working with binary data. Binary numbers can become extremely lengthy, and this is where octal proves its worth. It provides a more compact way to represent binary numbers because every octal digit equates to three binary digits (bits). For instance, the binary number 110 101 011 would be represented as 653 in octal. This condensed representation can make it easier to read and understand the value, especially when working with large binary numbers.
Even though octal is less frequently used than binary, decimal, or hexadecimal in modern computer systems, it has its niche uses. One such use is in Unix-based systems where it is applied in setting file permissions. For instance, the commonly used permission setting ‘755’ in Unix-based systems is an example of an octal number, where each digit represents the permissions for the owner, group, and others respectively.
Wile the octal number system might not be as universally employed as decimal or binary, its ability to represent binary data compactly and its specific uses in certain computer systems make it an important part of the computational number systems.