Fractions in octal number system

In this, We will discuss about how we represent fractional numbers in octal number system.

The octal point plays the same role as that of decimal point in decimal number system and binary point in the binary number system i.e. it separates the integer binary bits and fractional bits.

The procedure is similar to the procedure we followed to represent decimal fraction and binary fractions.

Each step involved in representation of the fractions in the octal number system is illustrated below.

Example 1: (407.304)₈ is the octal equivalent of ( 263.3828125 ) in decimal number system.

Step 1:

Write down the sequence of octal weights based on the number of digits in the given octal number separated by the octal point as shown below

8² 8¹ 8⁰8 ^-18 ^-28 ^-3← Weights

↑ ↑
MSD LSD

Step 2: Assign the values for the weights starting from LSD till the octal point and again starting from the octal point assign the integer values up to the MSD as done below.

8² 8¹ 8⁰8 ^-18 ^-28 ^-3← Weights

↑ ↑
MSB LSB

Step 3: Compute the product of individual octal digits and its associated weights to get the products which looks like the following

3 x 8 ^-1← LSD

0 x 8 ^-2

4 x 8 ^-3

7 x 8 ⁰

0 x 8 ¹

4 x 8 ²← MSD

Step 4: Add the individual products separated by the octal point as illustrated below

4 x 8 ²+ 0 x 8 ¹+ 7 x 8 ⁰. 3 x 8 ^-1 + 0 x 8 ^-2 + 4 x 8 ^-3

= 4 x 8 ²+ 0 x 8 ¹+ 7 x 8 ⁰. 3 x 8 ^-1 + 0 x 8 ^-2 + 4 x 8 ^-3

↑ ↑
MSD LSD

= 4 x 64+ 0 x 8+ 7 x 1. 3 x ( 1 / 8 ) + 0 x ( 1 / 64 ) + 4 x ( 1 / 512 )

= 256+ 0+ 7 . ( 0 . 375 ) + ( 0 ) + ( 0 . 0078125 )

= ( 263 . 3828125 )₁₀

Illustrated Examples