# Octal to Binary Converter

Enter an octal number below to convert it to binary.

## Binary Number:

### Steps to Convert to Binary

Learn how we calculated this below

## How to Convert Octal to Binary

Octal and binary numbers are foundational to computing systems. Converting from an octal number to a binary number is very common because base 8 offers a clean way to express three base 2 digits for each base 8 used, making it much easier to read.

Binary numbers, or base 2 numbers, consist of two digits: 0 and 1. Octal, or base 8, numbers consist of 8 digits: 0, 1, 2, 3, 4, 5, 6 & 7.

The base 8 system is often used in legacy computing applications because a single octal digit can represent three binary bits, which are cleanly divisible in 6, 12, 24, and 36-bit computer systems. Most modern computer systems, however, are 16, 32, or 64-bit systems, which are cleanly divisible into base 16 numbers.

Therefore, the hexadecimal system is more commonly used today.

To convert octal to binary, convert each digit to the equivalent binary number. Each octal digit is equal to three binary digits or bits.

### Octal Digit to 3-bit Binary Words

The following table shows the 3-bit word of binary digits for each octal digit.

octal digits converted to the equivalent 3-bit binary words
Octal Digit Binary Word
0 000
1 001
2 010
3 011
4 100
5 101
6 110
7 111

After converting each octal digit to a 3-bit word, place the words together to get the final number.

For example, let’s convert 7308 to binary.

78 = 1112
38 = 0112
08 = 0002

Putting it all together, the final binary value is:

111 011 000

After removing the spaces, you should end up with:

1110110002

## Octal to Binary Conversion Table

The table below shows a list of octal numbers converted to binary.

Octal numbers converted to the equivalent binary values
Octal Number Binary Number Decimal Number
0 0 0
1 1 1
2 10 2
3 11 3
4 100 4
5 101 5
6 110 6
7 111 7
10 1000 8
11 1001 9
12 1010 10
13 1011 11
14 1100 12
15 1101 13
16 1110 14
17 1111 15
20 10000 16
21 10001 17
22 10010 18
23 10011 19
24 10100 20
25 10101 21
26 10110 22
27 10111 23
30 11000 24
31 11001 25
32 11010 26
33 11011 27
34 11100 28
35 11101 29
36 11110 30
37 11111 31
40 100000 32
100 1000000 64
200 10000000 128
400 100000000 256
1000 1000000000 512
2000 10000000000 1024
4000 100000000000 2048