In this tutorial we will learn octal to decimal conversion of an integer number.

Before we dive into the main topic lets talk a little about Decimal and Octal Number System that we are going to work with in this tutorial.

A decimal number system consists of 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. So, any number that we use in our daily life is actually in decimal number system.

In Octal number system we use eight digits. 0, 1, 2, 3, 4, 5, 6 and 7 Octal implies base 8

How to convert an octal number into decimal number?

To convert an octal number into decimal form we have to multiply ones place by 8^{0} tens place by 8^{1} hundreds place by 8^{2} and so on…

Convert octal number 24_{(base 8)} into decimal form

The following table shows the places, octal number and the multipliers for the corresponding places.

place

tens

ones

octal

2

4

multiplier

8^{1}

8^{0}

= 2x8^{1} + 4x8^{0}
= 16 + 4
= 20

So, the required decimal number is 24_{(base 8)} = 20_{(base 10)} Alternatively, (24)_{8} = (20)_{10} Where, (base 10) means the number is in decimal number system and (base 8) means the number is in octal number system.

Convert octal number 156_{(base 8)} into decimal form

The following table shows the places, octal number and the multipliers for the corresponding places.

place

hundreds

tens

ones

octal

1

5

6

multiplier

8^{2}

8^{1}

8^{0}

= 1x8^{2} + 5x8^{1} + 6x8^{0}
= 64 + 40 + 6
= 110

So, the required decimal number is 156_{(base 8)} = 110_{(base 10)} Alternatively, (156)_{8} = (110)_{10} Where, (base 10) means the number is in decimal number system and (base 8) means the number is in octal number system.