Octal Arithmetic

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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 a octal number represents a 0 power of the base (8). Example 80

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

Example

Octal Number: 125708

Calculating Decimal Equivalent:

StepOctal NumberDecimal Number
Step 1125708((1 x 84) + (2 x 83) + (5 x 82) + (7 x 81) + (0 x 80))10
Step 2125708(4096 + 1024 + 320 + 56 + 0)10
Step 3125708549610

Note: 125708 is normally written as 12570.

Octal Addition

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

Octal Addition Table

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.

Example - Addition

Octal Addition Example

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

Octal Substraction Example

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