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

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 onâ€¦

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.

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.

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