Binary to Octal

Binary number systems and octal number systems are usually used in computing. The binary number has base two, whereas the octal number has base eight. In this tutorial, we will know about the binary and octal number system, Binary to Octal conversion, with few examples.

What is a Binary number system?

A binary number system refers to the number system that comprises two unique digits called 0 and 1. All the numbers from 2 to 9 are represented as 0 and 1 form. For example

(2)₁₀ = 0010

(5) ₁₀ =0011.

What is the Octal number system?

The octal number system refers to the number system that uses eight as its base. The base 8 number system is a system where values are represented using numbers 0 to 7. For example, (21)₈, (14)₈.

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

Binary to Octal Conversion

Converting by Hand

Remember a binary number series:

Binary numbers are usually represented as 0 and 1, such as 001, 100001, or even only 1. If you see this kind of one's and Zero's, usually called binary. However, many books represent binary numbers through a subscript "2", like 1110₂, which helps us understand the number without confusion.

The given subscript shows the base of the number. The binary number has a base value of two, and the octal number has a base value of 8.

Make a group of 1's and 0's in the binary number in sets of three from the right side.

As we know, there are two binary numbers and only eight octal numbers. You need three binary numbers to select each octal number, so you need to start from the right side to make your groups. For example, the binary number 110110100 would break down to 110 110 100.

If you don't have enough digits to make a set of three, add zeros to the left of the last digit.

The binary number 11010101 has eight digits, not a multiple of 3, but we can still convert it to an octal number. Add a zero to the last digit until it has three places. For example,

Binary number: 11010101

Grouping: 11 010 101

Adding extra zeros to make a group of three: 011 010 101

Add a number 4, 2, and 1 below each set of three numbers to calculate your place order

Every three binary numbers are arranging in an octal number system. The first number is for a 4, the second number is for a 2, and the third number is for a 1. To find the correct value, you need to write these numbers below three binary numbers. For example,

011 010 111
421 421 421
101
421
110 001 000
421 421 421

If there is a value one just above any placeholders, you need to write that number to start octal numbers.

If there is a one above 2, the value of an octal number is considered as 2. If there is a 0 above the one's place, the octal number does not take any value. For example,

Convert 111010100₂ to octal

First, you need to separate the binary number into three sets

111 010 100

Now, add placeholders

111 010 100

421 421 421

Mark each place

111 010 100

421 421 421

421 020 400

Add the new numbers in each set of three

Once you get the value of the octal number, you need to simply ass each set of three individually. So, for 011, which turns into 0,2,1, you get the value 3 (0 + 2+ 1). Consider the example mentioned above.

Convert 111010100₂ to octal

Mark each place

111 010 100

421 421 421

421 020 400

Add each set of three:

(4 + 2 + 1) (0+ 2+ 0) (0 + 2 + 1) = 7,2,3

Place the converted number from a final octal number

Dividing the binary number was +for make the problem easy. You can get the number in a single line., so your final octal number is

Convert 111010100₂ to octal

111 010 100

7 2 3

Now, putting the number back together = 723

Add subscript 8 for the final conversion

Without a proper notation, you can't differentiate octal or binary numbers. It means there is no other way except proper notation. So, you need to add a base 8 system to your final answer.

Convert 1110101002 to octal

111 010 100

7 2 3

Now, putting the number back together = (723)₈

Using shortcuts

Use an octal conversion chart to save time and burden.

You cannot apply this method in your school exams, but you can opt for this method to solve MCQs questions. As you already know, there are only eight possible combinations of numbers, so you can easily remember the chart. Usually, the thing you need to do is separate the numbers into a group of three numbers, then match them with the chart shown below.

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

Note: In the octal number system, numbers 8 and 9 do not exist since there are only eight digits.

If you are dealing with the decimal number system, keep the decimal where it is and work outward.

Let's consider an example if you will convert the binary number 11010.10 to an octal number. Generally, you work from right to left end in three sets, but with the decimal number system, you need to work away from the decimal point. So, for the number left to the decimal 11010, you need to start at the point and work left like (011 010). For the number located to the right of the decimal (.10), you need to start from the point and work right(100). If you are adding zeros, always add them in your working direction. You will get the given result 011 010 100. You can understand with the given example

101.01 = 101.010

1.00101 = 001. 001 010

1010101.00101 = 001 010 101. 001 010

Use the octal conversion chart to convert from octal to binary.

You need to remember the chart to solve the problem quickly. Use the given chat for the conversion of each octal digit into a set of three binary numbers.