Octal To Binary Conversion

1 oct = 1 bin

Want to convert from binary to octal instead?

Disclaimer: We've spent hundreds of hours building and testing our calculators and conversion tools. However, we cannot be held liable for any damages or losses (monetary or otherwise) arising out of or in connection with their use. Full disclaimer.

How to convert octal to binary (oct to bin)

Converting from octal (base-8) to binary (base-2) is a straightforward process, as both octal and binary are base-2 number systems. Each octal digit can be directly represented by a group of three binary digits.1. Understand the Octal to Binary Mapping: In octal, each digit corresponds to a group of three binary digits (bits). The mapping for octal digits to binary is below.

Octal	Binary
0	0000
1	0001
2	0010
3	0011
4	0100
5	0101
6	0110
7	0111

2. Split the Octal Number: Start by splitting the octal number into individual digits. If you have a multi-digit octal number, treat each digit separately.3. Convert Each Octal Digit to Binary: Take each octal digit and convert it to its corresponding three-digit binary representation using the mapping mentioned above. If the octal number has leading zeros, ensure that you include them in the binary conversion.4. Combine the Binary Digits: Once you've converted each octal digit into binary, combine the binary representations of all the octal digits to obtain the binary representation of the entire octal number.5. Remove Leading Zeros (Optional): If the binary representation contains leading zeros, you can choose to remove them to make the representation more concise. Leading zeros do not change the value of the binary number.

Example Conversion

Let's take a look at an example. The step-by-step process to convert 345 octal to binary is:

Understand the conversion formula:
Substitute the required value. In this case we substitute 345 for oct so the formula becomes:
Calculate the result using the provided values. In our example the result is: 345₈ = 3₈ 4₈ 5₈= 011₂ 100₂ 101₂ = 11100101

In summary, 345 octal is equal to 11100101 binary.

Converting binary to octal

Converting from binary (base-2) to octal (base-8) is a process that involves grouping binary digits into sets of three and then converting each group into its octal equivalent. Since octal is base-8, each octal digit represents three binary digits. Here's a step-by-step guide on how to convert binary numbers to octal.1. Group Binary Digits in Sets of Three: Start by dividing the binary number into groups of three digits from right to left. If there are any extra digits on the left that do not form a complete group of three, you can pad them with leading zeros. For example, if you have the binary number 1101011, you can group it as 001 101 011.2. Convert Each Group to Octal: Next, convert each group of three binary digits into its octal equivalent. To do this, match the binary group with the corresponding octal digit from the table below.

Binary	Octal
000	0
001	1
010	2
011	3
100	4
101	5
110	6
111	7

3. Combine Octal Digits: After converting each group, combine the octal digits to obtain the octal representation of the entire binary number.4. Remove Leading Zeros (Optional): If the octal representation has leading zeros, you can choose to remove them to make the representation more concise. Leading zeros do not change the value of the octal number.

Conversion Unit Definitions

What is a Octal?

The octal number system, also known as base-8, is another numerical representation used in mathematics and computer science. In the octal system, there are eight possible digits: 0, 1, 2, 3, 4, 5, 6, and 7. Each digit's value is determined by its position within the number, with each position representing a power of 8.

Similar to the binary and decimal systems, in the octal system, the rightmost digit holds the smallest place value and represents 8^0, which is 1. The next digit to the left represents 8^1, which is 8, and the pattern continues as you move to the left. For example, in the octal number 245, the digit '5' is in the ones place (8^0), '4' is in the eights place (8^1), and '2' is in the sixty-fours place (8^2). To convert an octal number to its decimal equivalent, you sum up the product of each digit with its corresponding power of 8. In the case of 245, it's 2*8^2 + 4*8^1 + 5*8^0, which equals 2*64 + 4*8 + 5*1, resulting in the decimal value 149.

The octal system is less commonly used today than the decimal or binary systems, but it has historical significance in the early days of computing. In the early 20th century, octal was frequently used in computer programming and debugging because it's relatively easy to convert between octal and binary, which was important in the context of early computer hardware. However, with the advent of more advanced programming languages and the adoption of the hexadecimal (base-16) system, octal's importance in computing has diminished. Nonetheless, it remains a valuable tool for certain applications and can be helpful in understanding the fundamentals of number systems and digital representation.

What is a Binary?

The binary number system, often referred to as base-2, is a fundamental numerical representation used in digital computing and information technology. Unlike the decimal system, which is based on powers of 10, the binary system relies on powers of 2, making it particularly well-suited for electronic devices and digital data storage. In the binary system, there are only two possible digits, 0 and 1, which are analogous to the on/off states of electronic switches. This simplicity is essential in the context of computing because it aligns perfectly with the binary nature of electronic circuits.

In binary, each digit represents a power of 2, starting from the right and increasing by one for each position to the left. For example, the rightmost digit represents 2^0 (which is 1), the next digit to the left represents 2^1 (which is 2), the next one represents 2^2 (which is 4), and so on. To convert a binary number to its decimal equivalent, you sum up the values of all the positions where a '1' appears. For instance, the binary number 1101 is equal to 12^3 + 12^2 + 02^1 + 12^0, which simplifies to 8 + 4 + 0 + 1, resulting in the decimal value 13.

The binary system is foundational in the field of computer science and digital electronics because it forms the basis for representing data, executing calculations, and transmitting information within electronic devices. It enables computers to process and store information in the form of binary code, where each piece of data, from text and numbers to images and videos, is ultimately represented as sequences of 0s and 1s. This universal language of computing facilitates the development of complex software, the operation of hardware components, and the exchange of data across the digital landscape, making it a cornerstone of modern technology.