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Octal Calculator
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The Octal number system is number system which is represented by base-8 number system and it ranges from 0 to 7. Once we reach 7 we run out of the digits and we replace 8 by 1. Octal number are given as: 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12......17, 21, 22,.... Octal Calculator adds, subtracts, divides and multiplies the given octal numbers. This calculates also converts the given octal numbers in decimal form to the base 10.

## Step by Step Calculation

Step 1 :

Read the given two octal numbers and find out what operation to be done.

Step 2 :

Four operations can be done to the given octal numbers: addition, subtraction, multiplication and division.

Addition : If the sum of given octal number is 7 or less than that, than the basic addition process is used. But if the sum is 8 then the number is taken as 10 and for every increase in number more than 8, the number is added by 1 to 10.

Subtraction: Subtraction operation in octal system is similar to that of basic subtraction operation method.

Multiplication: First multiply the given two octal numbers, after get the product go on subtracting the product by 8, till you get the value less than 8, add that value with the product to get the answer.

Division: Divide the given dividend with the divisor and get the quotient such that the each digits of the quotient is less than 8. the carry on on the division till you get the dividend less than divisor. The quotient is taken as the answer.

To Convert the given Octal numbers to decimal numbers:
First determine the decimal equivalent of any octal number, then multiply the positional value by the represented digit and add the result.

## Example Problems

1. ### Find the sum, difference of given two octal numbers:a = (5)8 and b = (3)8

Step 1 :

Given: a = (5)8

b = (3)8

To find the value of (a + b) and (a - b).

Step 2 :

a + b = (5)8 + (3)8

We know that by addition we get 5 + 3 = 8, but 8 is more than 7 so take the value of 8 as 10.

$\therefore$ (5)8 + (3)8 = (10)8

a - b = (5)8 - (3)8  = (2)8

The sum is a + b = (5)8 + (3)8 = (10)8

The difference is a - b = (5)8 - (3)8  = (2)8

2. ### Find the value of a*b and a/b of the given octal numbers where a = (6)8 and b = (5)8

Step 1 :

Given: a = (6)8

b = (5)8

Step 2 :

a*b = 6 $\times$ 5 = 30

30 - 8 = 22 > 8

22 - 8 = 14 > 8

14 - 8 = 6 < 8

So add the product and remainder 6

i.e  (a * b) = (6)8 * (5)= 30 + 6 =  36.

$\frac{a}{b}$ = $\frac{(6)_{8}}{(5)_{8}}$

= 1.14

$\therefore$ (a*b) = 36 and $\frac{a}{b}$ = 1.14

3. ### Convert the given number (57)8 in to decimal.

Step 1 :

Given octal number is (57)8

Step 2 :

(57)= 7 $\times$ 8+ 5 $\times$ 81

= 7 + 40

= 47