Octal to Binary Converter

To use octal to binary converter, type any octal value e.g. "76" and click on the Convert button and you will get the binary value of "111110" on right side. Type the numbers in the range from 0 to 7 for the octal values.

Octal to Binary Conversion:

• Octal Numeral System
• Binary Numeral System
• How to Convert Octal to Binary
• How to Convert Fractional Octal to Binary
• Octal to Binary Examples
• FAQs (Octal to Binary Conversion)
• Octal to Binary Table

Octal Numeral System

The octal number system is a positional number system that uses base 8.

This means it uses eight unique digits:

0, 1, 2, 3, 4, 5, 6, 7

8 and 9 are not the part of the octal number system. Every octal digit represents a position with the power of 8.

Example:

Octal number "4375.61" can be written as:

(4375.61)₈ = (4 × 8³) + (3 × 8²) + (7 × 8¹) + (5 × 8⁰) + (6 × 8^-1) + (1 × 8^-2) = 2048 + 192 + 56 + 5 + 0.75 + 0.015625 = (2301.765625)₁₀

Binary Numeral System

The binary numeral system uses the number 2 as it base or radix and it consists of only two numbers 0 and 1. The use of these binary numbers was prevalent since ancient times in medieval Golden Age and scientists like Al-Khwarizmi, Avicenna and Jamshid Al-Kashi made significant advances in algebra, mathematics, trignometry and geometry. Since then, the usage of binary numeral system has played a vital role in understanding modern scientific aspects e.g. detecting electrical signals where "0" represents the "OFF" state while "1" represents the "ON" state. Modern computers are completely based on binary numeral system and all the data is interpreted in binary formats. The numbers can be represented in binary format using the powers to the base 2 i.e. 2⁰, 2¹ etc.

The number "1" is represented in binary as "01" and the number "2" is represented in binary as "10" and every digit in the binary number is called as 1 bit. 1 Byte is equal to 8 bits.

Example:

Binary value (101101.001)₂ written as powers of 2:

How to Convert Octal to Binary

To convert octal to binary follow the following steps:

• Step-1: Each octal digit maps to exactly 3 bits. Hence separate the octal digits and represent every digit in 3 binary bits. Every bit position refers to the power of 2.

• Step-2: Determine which bits needed to be set to high "1" and which bits needed to be low "0" to correctly reflect the octal digit.

• Step-3: Combine all the binary bits together to get the final binary value.

How to Convert Fractional Octal to Binary

Please consider the following steps to convert fractional octal value to binary:

• Step-1: Get the fractional value from the octal number. For example, for the octal number "37.71", 0.71 is the fractional part.

• Step-2: Represent each digit as 3 bits. For example, 7 is represented as 111 and 1 is represented as 001

• Step-3: Combine the bits to get the final fractional binary value i.e (0.111001)₂

Octal to Binary Examples

Example 1: Convert the octal value "276" to binary.

Example 2: Convert the octal value "675" to binary.

Example 3: Convert the octal value "3767" to binary.

Example 4: Convert octal value "173.61" to binary.

Example 5: Convert octal value "7657.573" to binary.

Frequently Ask Questions: Octal to Binary Conversion

Q1: Convert octal number (745)₈ to binary ?

Since 7 = 111, 4 = 100, and 5 = 101, therefore binary value is (111100101)₂

Q2: Why do we start grouping bits in sets of 3 while converting octal to binary?

Because 2³ = 8, therefore, grouping binary bits into 3-bit chunks creates values from 0–7 which exactly correspond to a single octal digit. It also ensures that no information or data loss is occurred.

Q3: Add two octal digits 37 and 75 and provide the result in binary ?

(37)₈ = (3 × 8¹) + (7 × 8⁰) = 24 + 7 = (31)₁₀ (decimal)

(75)₈ = (7 × 8¹) + (5 × 8⁰) = 56 + 5 = (61)₁₀ (decimal)

Add the decimal equivalent: 31 + 61 = 92

Convert the decimal result into binary, you can also check Decimal to Binary Converter for the detailed understanding.

• 92/2 = 46, Remainder = 0

• 46/2 = 23, Remainder = 0

• 23/2 = 11, Remainder = 1

• 11/2 = 5, Remainder = 1

• 5/2 = 2, Remainder = 1

• 2/2 = 1, Remainder = 0

• 1/2 = 0, Remainder = 1

Now combine all the remainders from last value to the first,

Binary value = (1011100)₂

Q4: Right shift the octal value "7765" by 5 bits and do padding on the left with 1, what is the final result in binary?

As each octal digit can be represented by 3 bits:

7 = 111, 7 = 111, 6 = 110, 5 = 101, Therefore binary value is (111111110101)₂

Right shift by 5 bits and pad 1s on the left side:

(111111110101)₂ >> 5 = (111111111111)₂

The octal value of the above shifted value is 7777.

Q5: How to convert octal value 17.71 to binary?

Convert all octal digits to 3 bits binary and combine them:

1 = 001, 7 = 111, therefore, binary value is:

(001111.111001)₂ = (1111.111001)₂

Octal to Binary Conversion Table

by Wasim Khan and it was last modified on August 25, 2025

Related Conversions

Please find the related numeric conversions.

• ASCII Text to Binary
• ASCII Text to Decimal
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• Binary to Hex
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• Decimal to ASCII Text
• Decimal to Binary
• Decimal to Hex
• Decimal to Octal
• Hex to ASCII Text
• Hex to Binary
• Hex to Decimal
• Hex to Octal
• Octal to Decimal
• Octal to Hex

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