Octal to Decimal conversion of an integer number

Conversion

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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 80
tens place by 81
hundreds place by 82
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.

placetensones
octal24
multiplier8180

= 2x81  +  4x80
= 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.

placehundredstensones
octal156
multiplier828180

= 1x82  +  5x81  + 6x80
= 64 + 40 + 8
= 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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