Convert Octal to Binary

In mathematics, numerous number systems are used to write numbers, such as the binary number system (base 2), the octal number system (base 8), the decimal number system (base 10), and the hexadecimal number system (base 16). The process of changing a number from base-8 to base-2 is known as octal to binary conversion. There are direct and indirect techniques for converting an octal number to a binary number. In an indirect technique, you must first convert an octal number into another number system (e.g., decimal or hexadecimal), then into binary number by converting each digit into binary number from the hexadecimal system and utilizing the conversion system from decimal to binary number.

Definition of Octal Number System and Binary Number System

The octal number system is a base - 8 number system. It implies that this number system includes a total of 8 symbols such as 0, 1, 2, 3, 4, 5, 6, and 7 to represent any values. In computer, the octal number system is represented as:

• Writing 8 as a suffix of the value (eg. 765₈).

On the other hand, the binary number system is a base-2 number system that primarily includes only 2 symbols such as 0 and 1 to represent any values. In computer, the binary number system is represented as:

• Writing 2 as a suffix of the value (eg. 765₂).

Read on to know how to convert the octal number system to the binary number system.

How To Convert Octal To Binary?

Conversion of octal to binary is a straightforward process because octal numbers are shortened versions of binary strings. For the process of conversion, every digit in the given octal number should be converted to a 3-bit binary number and hence arriving at the binary equivalent of the octal number. Octal numbers can also be converted to the equivalent binary number indirectly (first decimal then binary). Following is the table representation for the conversion of octal numbers into binary numbers and vice versa directly.

Let us understand octal to binary numbers using the direct method with an example:

Example 1: Convert 76₈ to its equivalent binary number.

Solution: Given an octal number i.e. 76₈. With the help of the table given below, we can write 76₈ in binary number as 111110₂.

Therefore, 76₈ = 111110₂.

Octal To Binary Conversion (Indirect Method)

Conversion of octal to binary using an indirect method is a two-way process. In the indirect method, we will first convert the given octal number into its equivalent decimal number and in the next step, we will convert the decimal number into its equivalent binary number.

Let us first understand Octal to Decimal conversion.

To convert the octal number (base - 8) to the decimal number (base - 10), we will use the octal place value to add the base-10 value of each digit.

Each time you move towards the left in the octal number system, the value increases eight times.

In the octal number, the digit values go from 0 to 7, the numbers 8 and 9 are not allowed.

Decimal To Binary Conversion

Following are the steps to convert the obtained decimal number into its equivalent binary number.

• Step 1: Divide the obtained decimal number by 2 and write down the remainder.

• Step 2: Now, divide the quotient that is obtained in the above steps by 2, and note the remainder again.

• Step 3: Repeat the above two steps until you get 0 as the quotient.

• Step 4: Now, list down the remainder in such a way that the last remainder is written first, followed by the rest in the reverse order.

This process can also be understood in another way which states that the Least Significant Bit (LSB) of the binary number will be placed at the top and the Most Significant Bit (MSB) will be placed at the bottom. This number obtained will be the binary value of the given decimal number.

Octal To Binary Conversion Example (Indirect Method)

Question: Convert 634₈ to a binary number.

Solution: We will first convert the given octal number into its equivalent decimal number. Let us learn the steps.

Step 1: Write down the given octal number, expressing it as a power of 8 starting from right to left for each integer value. The power of 8 from the right side starts with 0 as shown below.

68² + 3 8¹ + 48º

Step 2: Write down the place value of each digit of the given octal number.

• 8º = 4

• 8¹ = 3

• 8² = 6

Step 3: Multiply the above-obtained power of 8 values with its respective octal digit as shown below:

• 6 64 = 384

• 3 8 = 24

• 4 1 = 4

Step 4: Sum up the resultant values obtained in the above step after the multiplication of each octal digit and the octal weights or power of 8 values.

= 384 + 24 + 4

= 412

Hence, 634₈ = 412₁₀

Now, we will convert the resultant decimal number into its equivalent binary number.

Decimal Number = 412₁₀

Therefore, the binary equivalent for the given octal number 634₈ is 110011100₂.

Answer: 634₈ = 110011100₂

Octal To Binary Converter

Octal to binary converter is an easy-to-use online converter that enables you to convert the given octal numbers into their equivalent binary number in a fraction of seconds. The converter will give you the binary equivalent of the given octal number.

Solved Example

1. Convert (305)₈ to its equivalent binary number using the direct method.

Solution:

Given an octal number i.e. (305)₈. With the help of the table given above, we can write (305)₈ in binary number as (011 000 101)₂.

Therefore, (305)₈ = (011 000 101)₂.

2. Convert (145)₈ to a binary number using the indirect method.

Solution:

We will first convert the given octal number into its equivalent decimal number. Let us learn the steps.

Step 1: Write down the given octal number, expressing it as a power of 8 starting from right to left for each integer value. The power of 8 from the right side starts with 0 as shown below.

18² + 4 8¹ + 58º

Step 2: Write down the place value of each digit of the given octal number.

• 8º = 1

• 8¹ = 4

• 8² = 5

Step 3: Multiply the above-obtained power of 8 values with its respective octal digit as shown below:

• 1 64 = 64

• 4 8 = 32

• 5 1 = 5

Step 4: Sum up the resultant values obtained in the above step after the multiplication of each octal digit and the octal weights or power of 8 values

= 64 + 32 + 5

= 101

Hence, (145)₈ = (101)₁₀

Now, we will convert the resultant decimal number into its equivalent binary number.

Decimal Number = (101)₁₀

Therefore, the binary equivalent for the given octal number (145)₈ is (1100101)₂

(145)₈ = (1100101)₂

Practice Question MCQs

1. In an octal number system, what is the maximum value of a single digit?

1. 5

2. 6

3. 7

4. 8

Answer: D) In every number system, the maximum value is one less than the value of the base. Because the basis in an octal number system is 8, the maximum value of a single digit is 7. It accepts digits ranging from 0 to 7.

2. _________ is the maximum number of bits required to express an octal number in binary.

1. 1

2. 2

3. 3

4. 4

Ans: The octal number system has just eight digits. As a result, in binary format, three bits are sufficient to represent any octal integer.

Conclusion

Computers work with binary systems but strings of just 0 and 1 can be too long and unstructured for us. Binary to octal conversion makes it possible to compress these long strings and makes them easier to work with. Octal numbers (base-8) are sort of the middle ground between the binary system (base-2) computers use and decimal system (base-10) humans use.