Expressing a number using the binary system requires the use of many more digits than in the decimal system. The many binary digits can be difficult to read; therefore other related numbering systems were developed.
The octal numbering system uses a base of 8. This number is used because 8 bits of data make up a byte of information. The digits range from 0 to 7. This system provides an easy method of handling large binary numbers. One octal digit can be used to express three binary digits (see chart).
Like all other numbering systems, each digit in the octal system has a weighted decimal value according to its position. Octal numbers are easy to convert to binary numbers. Each digit of an octal number is converted by assembling the 3 bit groups for each digit (see example).
Octal Number 462
4 = 100
6 = 110
2 = 010
Equivalent Binary Number = 100 110 010
Allen-Bradley PLC-5 processors use octal-based I/O addressing but the SLC 500 and Logix controllers used the decimal number system.