Octal to Decimal conversion of a number having fractional part

Conversion

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In this tutorial we will learn octal to decimal conversion for a floating point number i.e., a number with fractional part.

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 a octal number with fractional part into decimal number?

To convert a octal number having integer and fractional part into decimal form we have to multiply the integer part
ones place with 80
tens place with 81
hundreds place with 82
ans so on...
and the fractional part
tenths place by 8-1
hundredths place by 8-2
and so on...

Convert octal number 0.01(base 8) into decimal form.

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

placeonesDecimal
Point
tenthshundredths
octal0.01
multiplier808-18-2

= 0x80 + 0x8-1 + 0x8-2
= 0 + 0 + 0.015625
= 0.015625

So, the required decimal number is
0.01(base 8) = 0.015625(base 10)
Alternatively, (0.01)8 = (0.015625)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 7.12172(base 8) into decimal form.

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

placeonesDecimal
Point
tenthshundredthsthousandthsten
thousandths
hundred
thousandths
octal7.12172
multiplier808-18-28-38-48-5

= 7x80  +  1x8-1  +  2x8-2  +  1x8-3  +  7x8-4  +  2x8-5
= 7 + 0.125 + 0.03125 + 0.001953125 + 0.001708984375 + 0.00006103515624
= 10.1599...
= 10.16 (approx. value)

So, the required decimal number is
7.12172(base 8) = 10.16(base 10) (approx. value)
Alternatively, (7.12172)8 = (10.16)10 (approx. value)
Where, (base 10) means the number is in decimal number system and (base 8) means the number is in octal number system.