Octal Arithmetic

Octal Number System

Following are the characteristics of an octal number system.

Uses eight digits, 0,1,2,3,4,5,6,7.

Also called base 8 number system.

Each position in an octal number represents a 0 power of the base (8). Example: 8⁰

Last position in an octal number represents an x power of the base (8). Example: 8^x where x represents the last position - 1.

Example

Octal Number − 12570₈

Calculating Decimal Equivalent −

Step	Octal Number	Decimal Number
Step 1	12570₈	((1 × 8⁴) + (2 × 8³) + (5 × 8²) + (7 × 8¹) + (0 × 8⁰))₁₀
Step 2	12570₈	(4096 + 1024 + 320 + 56 + 0)₁₀
Step 3	12570₈	5496₁₀

Note − 12570₈ is normally written as 12570.

Octal Addition

Following octal addition table will help you to handle octal addition.

To use this table, simply follow the directions used in this example: Add 6₈ and 5₈. Locate 6 in the A column then locate the 5 in the B column. The point in sum area where these two columns intersect is the sum of two numbers.

6₈ &plus; 5₈ = 13₈.

Example − Addition

Octal Subtraction

The subtraction of octal numbers follows the same rules as the subtraction of numbers in any other number system. The only variation is in borrowed number. In the decimal system, you borrow a group of 10₁₀. In the binary system, you borrow a group of 2₁₀. In the octal system you borrow a group of 8₁₀.

Example − Subtraction