# Octal to Decimal

#### Octal Number System

Base 8 number system which consists numbers {0, 1, 2, 3, 4, 5, 6, 7}.

#### Decimal Number System

Base 10 number system which consists numbers {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.

Decimal Number System

Octal Number System

## Octal to Decimal Conversion Procedure

1. Write down the octal numbers.

2. Find the position of every digit. We should count the position from the right direction of the number. And the position count starts from 0.

#### Example

**134** - position of 4 = 0, 3 = 1, 1 = 2.

**501** - position of 1 = 0, 0 = 1, 5 = 2.

3. Multiply every digit with 8 to the power of their corresponding position. (8 ^{position})

4. Finally, calculate the sum of all the multiples.

## Example

#### (16)_{8} to decimal

position = {1-1, 6-0}

= 1 x 8 ^{1} + 6 x 8 ^{0}

= 8 + 6

= (14)_{10}

## Example

#### (7777)_{8} to decimal

position = {7-3, 7-2, 7-1, 7-0}

**f** equivalent decimal = 15

= 7 x 8 ^{3} + 7 x 8 ^{2} + 7 x 8 ^{1}+ 7 x 8 ^{0}

= 7 x 512 + 7 x 64 + 7 x 8 + 7 x 1

= 3584 + 448 + 56 + 7

= (4095)_{10}