Binary to Octal Converter

Enter the binary number you want to convert to octal.

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Number Grouping

Calculation Steps:

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How does binary to octal conversion work?
Binary to octal conversion formula
Conversion process
Examples
Binary to octal conversion table
Frequently Asked Questions

How does binary to octal conversion work?

The binary system is base 2 and the octal system is base 8. To convert a binary number to octal, group the binary digits into blocks of 3 starting from the right (adding zeros to the left if necessary). Then, replace each group of 3 bits with its equivalent octal value (0–7).

Binary to octal conversion formula

For a binary number of n digits:

Octal = (\underset{3 bits}{group}) \to O ₁_{} O ₂_{} \dots O ₖ_{}

Where each block of 3 bits is converted into an octal digit O_j (0–7).

Conversion process

Write the binary number and group it into blocks of 3 digits starting from the right (add zeros to the left if necessary).
Convert each block of 3 bits into its decimal equivalent value (from 0 to 7).
Combine the obtained values to form the number in base 8 (octal).

Examples

Example 1: convert 101110₂ to octal

101110₂ → group into blocks of 3 bits: 101 110

101₂ = 5₈, 110₂ = 6₈

Result: 101110₂ = 56₈.

Example 2: convert 1110011₂ to octal

1110011₂ → group into blocks of 3 bits: 111 001 011

111₂ = 7₈, 001₂ = 1₈, 011₂ = 3₈

Result: 1110011₂ = 713₈.

Binary to octal conversion table

Quick reference values for short binary numbers.

Binary (base 2) to octal (base 8) references
Binary	Octal
`0`	0
`1`	1
`10`	2
`11`	3
`100`	4
`101`	5
`110`	6
`111`	7
`1000`	10
`1001`	11
`1010`	12
`1011`	13
`1100`	14
`1101`	15
`1110`	16
`1111`	17
`10000`	20
`100000`	40
`1000000`	100
`10000000`	200
`100000000`	400
`1000000000`	1000
`10000000000`	2000

Frequently Asked Questions

How do you convert a binary number to octal?

To convert a binary number to octal, group the binary digits into blocks of 3 starting from the right. Then, replace each block with its equivalent octal value (0–7).

Why are bits grouped in sets of 3?

Because each octal digit represents exactly 3 bits. This makes the conversion between binary and octal straightforward and easy.

Explore More

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