# 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: 8x 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. 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 + 58 = 138.
``` ## 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  