Binary to Octal Converter
The binary to octal converter quickly converts any binary number to its equivalent base-8 number.
What Is a Binary Number System?
A binary number system is a type of number system that deals with zero and one numeric value. This system is known as a base-2 system because its numbers represent only 0s and 1s.
What Is an Octal Number System?
An octal number system is another type of number system that deals with 0-7 numeric values. This system is also known as the base-8 number system. All the combinations of numbers in this system will be from 0 to 7, and there will not be any presence of 8 or 9 in any combination.
How to Convert Binary to Octal?
Using our binary to octal converter above, you can effortlessly convert any binary to octal. Below are a few methods for manually converting binary numbers to octal numbers.
Method 1: By Using Binary to the Octal Conversion Table
- Take a binary number
- Make groups of three bits of the given binary number from right to left.
- If the final set of three bits doesn’t form a group of three, add zeros to the left.
- Compare the values from the binary to an octal conversion table.
- The obtained number will be the octal number.
Below is the binary to octal table:
| Binary to Octal Table | |
| Binary | Octal |
| 000 | 0 |
| 001 | 1 |
| 010 | 2 |
| 011 | 3 |
| 100 | 4 |
| 101 | 5 |
| 110 | 6 |
| 111 | 7 |
Method 2: Without Using a Conversion Table
The conversion of binary to octal can also be done without using a conversion table. Follow the steps below:
- Take a binary number
- Convert the binary number to decimal.
- Convert the obtained decimal number to octal.
- The obtained number will be the octal number.
Binary to octal conversion examples
Here are a few binary to octal conversion examples.
Example 1: By using Table
Convert (11110100001)2 to an octal number.
Solution
Step 1: Make groups of three bits of the given binary number from right to left.
(11110100001)2 = 11 110 100 001
Step 2: Add a zero to the left of the first set to complete it.
(11110100001)2 = 011 110 100 001
Step 3: Compare the binary values in the conversion table and write equivalent octal values.
(11110100001)2 = 36418
Example 2: Without using Table
Convert (11010100001)2 to an octal number.
Solution
Step 1: Convert the given binary number to a decimal number.
(1101010)2 = (1 x 26) + (1 x 25) + (0 x 24) + (1 x 23) + (0 x 22) + (1 x 21) + (0 x 20)
(1101010)2 = (1 x 64) + (1 x 32) + (0 x 16) + (1 x 8) + (0 x 4) + (1 x 2) + (0 x 1)
(1101010)2 = (64) + (32) + (0) + (8) + (0) + (2) + (0)
(1101010)2 = 64 + 32 + 8 + 2
(1101010)2 = 106
Step 2: Now convert the obtained decimal number to octal.
| Divided by | Quotient | Remainder |
| 8 | 106 | |
| 8 | 13 | 2 |
| 1 | 5 |
10610 = 1528
Hence,
(1101010)2 = 1528
You can also use our octal to binary converter to convert any octal number into a binary number.