# Octal to Decimal

## Octal to Decimal

When an octal number with a base of 8 needs to be changed into a decimal number with a base of 10, this process is known as octal to decimal conversion. The conversion from octal to decimal is identical to the modifications from decimal to octal, hexadecimal to octal, binary to octal, and so on. For a better understanding, let's study more about the conversion techniques and work through a few cases.

## Octal to Decimal Conversion: What Is It?

When determining a number's equivalent in the number system, we convert octal numbers to decimals. The number system is divided into four different categories: the binary, octal, decimal, and hexadecimal systems. Every number system contains a set of base numbers that can be used to determine the kind of number it is. These base numbers also aid the conversion of octal to decimal. Octal numbers have a base of 8, while decimal numbers have a basis of 10.

## How to change an octal number to a decimal

A regular decimal number is created by adding the digit sum to 10n.

Example:

Each digit multiplied by its corresponding 10n yields 137 in base 10:

13710 = 1×102+3×101+7×100 = 100+30+7

The only difference is that each digit in an octal number counts as 8n rather than 10n. They are multiplying each hex digit by the matching 8n value.

Octal

base 8

Decimal

base 10

0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
10 8
11 9
12 10
13 11
14 12
15 13
16 14
17 15
20 16
30 24
40 32
50 40
60 48
70 56
100 64

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