The octal number system is a positional numeral system that uses a base of eight. It is also known as base eight system. In this system, the digits range from 0 to 7. Each digit's place value is based on powers of eight. The rightmost digit represents the units' place, the next digit to the left represents the eights' place, the next digit to the left represents the sixty-fours' place, and so on.
To convert a number from decimal (base ten) to octal, the number is divided successively by eight. The remainders from each division, read in reverse order, form the octal equivalent. Conversely, to convert an octal number to decimal, the digits are multiplied by their corresponding powers of eight, and the results are added together.
Octal numbers are commonly used in computer programming, especially when dealing with binary code. Since the base eight system is a concise representation of binary numbers, it provides an easier way to read and write long sequences of zeros and ones. Typically, octal numbers are prefixed with a leading zero to distinguish them from decimal numbers. For example, 0457 is an octal representation, while 457 is decimal.
The octal number system is considered a compact and efficient way to represent binary data, as it simplifies long binary strings and reduces their complexity. It is widely used in computer programming, particularly in low-level programming languages and system software.
