Binary To Octal

In binary to octal conversion, we convert numbers from the base 2 system to the base 8 system. We cannot convert binary to octal directly, so we first convert the binary number to decimal, and then convert the decimal number to its octal equivalent. Computers often use binary numbers in the form of bits and bytes, because they operate using only 0 and 1. Similarly, octal numbers are used in electronics. Before converting, we need to understand both octal and binary numbers.

What are Binary Numbers?

Numbers written in base 2 are called binary numbers. They have only two digits, 0 and 1. We represent them as a₂, where a is a combination of 0 and 1.

What are Octal Numbers?

Numbers written in base 8 are called octal numbers. They use only the digits 0 to 7. The digits 8 and 9 do not appear in the octal system. We write them as a₈, where a is a number containing the digits 0 to 7.

Why Convert Binary to Octal?

Converting binary to octal simplifies long binary numbers, speeds up calculations, and helps with programming and electronics troubleshooting. Many competitive exams and school or board syllabus include questions that assess your ability to perform these conversions quickly and correctly.

Basic Formula for Binary to Octal Conversion

Follow this simple method: Divide the binary digits into three groups, starting from the right, then write the corresponding octal number for each group. If a group has fewer than three digits, add an extra 0 to the left.

Binary to Octal Conversion

In the study of number systems, you come across different types of numbers such as binary, octal, decimal, and hexadecimal. To convert a binary number to octal, follow these steps:

Take the binary number you want to convert.

Multiply each binary digit by 2ⁿ⁻¹, where n is the position of the digit starting from the right.

Add the results to get the equivalent decimal number for the binary value.

Divide this decimal number by 8.

Record the remainder.

Repeat the division process with the new divisor until the divisor is zero.

Arrange all the remainders in reverse order.

The final number you get is the octal equivalent of the original binary number.

Binary and Octal Number Systems

Binary and octal are two different number systems that use different sets of symbols to express numbers.

To make this clear, let us refer to our familiar decimal system, which uses the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 to represent all numbers.

Similarly, the binary number system uses only two symbols, 0 and 1 (called base 2) to represent numbers. On the other hand, the octal system (or base 8 system) uses eight symbols: 0, 1, 2, 3, 4, 5, 6, and 7.

As shown in Table I, each octal digit can be represented using three binary digits.

How to Convert a Binary Number to Octal
Converting a binary number to octal is easy:

Start with the rightmost digit and group the binary digits into sets of three.

Convert each group to the corresponding octal digit using Table I.

If necessary, add leading zeros to complete the group of three.

The process of converting binary to octal is quite simple. Let’s look at an example by converting the binary number

(11001)2

(11001)2

to octal.

First, we arrange the digits into three-bit groups:

011

001

011 001,

adding leading zeros to complete the first group.

Now, using Table I, convert each group to its octal equivalent:

011→3
011→3
001→1
001→1

Thus, the octal representation of the binary number

(11001)2

will become

(31)8

(31)8

If you want to find conversions to hexadecimal or decimal, check out the binary-to-hexadecimal and binary-to-decimal tools.

How to Convert Octal to Binary
Converting an octal number to binary is also easy. Simply replace each octal digit with its corresponding 3-bit binary number from Table I.

For example, let’s convert
(715)8
(715)8 to binary:

From Table I,
7
7’s binary equivalent is
111
111.

The binary equivalents for other digits are:
1→001
1→001
5→101
5→101

So,
(715)8
(715)8
become
(111001101)2
(111001101)2

Cross-Disciplinary Uses

Converting binary to octal is not only helpful in mathematics but also in physics, electronics and computer science. Students preparing for competitive exams like JEE or Olympiads benefit greatly from mastering this skill when dealing with number systems and coding questions.

Speed ​​Trick or Shortcut

A simple shortcut: always create groups of three binary digits starting from the right side (LSB side). If digits are missing, simply add zeros to the left. Refer to the table above to quickly find the octal value for any triplet. Many students use this method during exams to save time and reduce calculation errors – which is similar to the strategies taught in live Vedantu sessions.

FAQs: Frequently Asked Questions