The conversion between binary numbers and octal numbers is an effortless and straightforward task. Let’s start.

Key Questions:

  • Convert octal numbers into binary numbers
  • Convert binary numbers into octal numbers
  • Convert octal fractional numbers into binary fractional numbers
  • Convert binary fractional numbers into octal fractional numbers
Octal numbers0001020304050607
Binary numbers00011011100101110111

Binary to Octal Conversion:

The conversion method is to make a group of three bits. But why do we make a group of 3 bits? Because 3 bits number in binary the total values can be expressed are 2n or largest possible value for a 3 bit number is 2n-1=7. The total digits or unique symbols in base 8 (octal) system are 8.

For integers start making groups from right to left.

Binary to octal conversion solved example

Example 01011101)2

010 011 101

We have a 8 bit number. Start making group of 3 bits from right. You can make 2 groups easily. For 3rd 3 bit group we have to add extra 0. As shown above

For fractional part start making group from left to right.

Example 0.1111000111)2

0.111 100 011 100


Making group of 3 bits

110 111 011 . 110 100

Binary number110111011.110100
Octal number673.64

Answer 110111011.11010)2=673.64)8

Example#02: 101111001.010101)2

Making group of 3 bits

101 111 001.010 101






Answer 110111011.11010)2=571.25)8

Example#03: 1111110011111001)2=?)8

Making group of 3 bits

001 111 110 011 111 001

Note: add two zeros on the left in order to make group of 3 bits.

Binary number001111110011111001
Octal number176371

Answer 1111110011111001)2=176371)8

Octal to Binary Conversion:

The conversion method is to take individual octal digit and convert it in binary. Make sure convert in the way that each octal digit should represent in 3 bit binary group.

For example if

1)8 =001)2 right way

1)8 =1)2 wrong way

Note: this is wrong for this conversion technique only. Otherwise it is obviously the same.

1)8 =1)2


Represent each octal digit in 3 bit binary number.

Octal number673.64
Binary number110111011.110100

Answer 673.64)8= 110111011.110100)2

Or 673.64)8= 110111011.1101)2

Note: you can remove the right most 0s that are unnecessary.

Example#02: 571.25)8= ?)10

Represent each octal digit in 3 bit binary number.

Octal number571.25
Binary number101111001.010101

Answer 571.25)8= 101111001.010101)2

Example#03: 176371)8=?)2

Represent each octal digit in 3 bit binary number.

Octal number176371
Binary number001111110011111001

Answer 176371)8= 1111110011111001)2

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