OCTAL NUMBER SYSTEM

OCTAL NUMBER SYSTEM

The octal, or base 8, number system is a common system used with computers. Because of its relationship with the binary system, it is useful in programming some types of computers.

Look closely at the comparison of binary and octal number systems in table 1-3. You can see that one octal digit is the equivalent value of three binary digits. The following examples of the conversion of octal 2258 to binary and back again further illustrate this comparison:



Table 1-3. - Binary and Octal Comparison



Unit and Number

The terms that you learned in the decimal and binary sections are also used with the octal system.

The unit remains a single object, and the number is still a symbol used to represent one or more units.

Base (Radix)

As with the other systems, the radix, or base, is the number of symbols used in the system. The octal system uses eight symbols - 0 through 7. The base, or radix, is indicated by the subscript 8.

Positional Notation

The octal number system is a positional notation number system. Just as the decimal system uses powers of 10 and the binary system uses powers of 2, the octal system uses power of 8 to determine the value of a number's position. The following bar graph shows the positions and the power of the base:



Remember, that the power, or exponent, indicates the number of times the base is multiplied by itself. The value of this multiplication is expressed in base 10 as shown below:



All numbers to the left of the radix point are whole numbers, and those to the right are fractional numbers.