Octal to Binary

Octal to Binary Conversion

Octal to Binary conversion is an essential part of the number system, where octal numbers (base 8) are converted into binary numbers (base 2). This process is crucial for simplifying complex binary data into manageable units, which are vital in computer systems and digital electronics.

What are Binary Numbers?

Binary numbers use only two digits: 0 and 1. These digits are fundamental in computing, where all data—whether numbers, text, images, or media—is processed and stored using the binary system.

What are Octal Numbers?

Octal numbers are based on the number 8, using digits from 0 to 7. They are often used to represent binary data more compactly in various computational applications.

Methods to Convert Octal to Binary

There are two main methods to convert octal numbers into binary:

• Method 1: Convert octal to decimal and then decimal to binary.
• Method 2: Direct octal to binary conversion using binary representations for each octal digit.

Method 1: Octal to Decimal and Then Decimal to Binary

Steps:

1. Convert the octal number to its decimal equivalent by multiplying each digit with the corresponding power of 8.
2. Convert the resulting decimal number to binary by dividing it by 2 and noting down the remainders in reverse order.

Method 2: Direct Octal to Binary Conversion

In this method, each digit of the octal number is directly converted into its 3-bit binary equivalent. For example, 1 becomes 001, 2 becomes 010, and so on.

Octal to Binary Table

Solved Examples of Octal to Binary Conversion

Example 1: Convert (123)₈ to binary

Binary equivalent: 1010011₂

Example 2: Convert (4321)₈ to binary

Binary equivalent: 100011010001₂

Example 3: Convert (41)₈ to binary

Binary equivalent: 100001₂

Example 4: Convert (10)₈ to binary

Binary equivalent: 1000₂

FAQs

What is an octal number system?

The octal number system is a base-8 system using digits 0 to 7. It is often used in computing as a shorthand for binary data.

What is a binary number system?

The binary system is a base-2 number system that uses only 0 and 1 to represent data. It is essential in computing and digital electronics.

How do I convert octal to binary?

You can convert octal numbers to binary by either converting them to decimal first and then to binary or by converting each octal digit into its binary equivalent.