# Octal to Binary Converter

To use this octal to binary conversion tool, you must type an octal value like 5432 into the left field below and hit the Convert button. The converter will give you the binary equivalent of the given octal.

swap conversion: Binary to Octal Converter
Octal to binary conversion result in base numbers

## The Octal System

The octal number system (or shortly oct) uses the number 8 as its base (radix). As a base-8 numeral system, it uses eight symbols: The numbers from 0 to 7, namely 0, 1, 2, 3, 4, 5, 6 and 7. Although it was used by some native American tribes until the 20th century, the octal system has become popular in the early ages of computing as a language of computer programming. This is because the octal system shortens binary by simplifying long and complex chains of binary displays used by computers.

The octal system is mainly used for counting binary in groups of three: Each octal digit represents three binary digits. Since 8 is 2 to the third power (23), the octal system became a perfect abbreviation of binary for machines that employ word sizes divisible by three - which were 6-bit, 12-bit, 24-bit or 36-bit. Nowadays, most modern systems use hexadecimal rather than octal. However, octal numbers are an important part of basic knowledge in electronics.

## Binary System

The binary numeral system uses the number 2 as its base (radix). As a base-2 numeral system, it consists of only two numbers: 0 and 1.

While it has been applied in ancient Egypt, China and India for different purposes, the binary system has become the language of electronics and computers in the modern world. This is the most efficient system to detect an electric signal’s off (0) and on (1) state. It is also the basis for binary code that is used to compose data in computer-based machines. Even the digital text that you are reading right now consists of binary numbers.

Reading a binary number is easier than it looks: This is a positional system; therefore, every digit in a binary number is raised to the powers of 2, starting from the rightmost with 20. In the binary system, each binary digit refers to 1 bit.

## How to Convert Octal to Binary

Converting from octal to binary has a very straightforward method because octal numbers are shortened versions of binary strings. Remember that each octal digit represents three binary digits. Therefore, one octal digit should give three binary digits (bits). While octal can be converted to binary indirectly (first the to the decimal, then to binary), a direct method to convert octal to binary with steps is as follows:

• Step 1: Write down the octal number separating the digits. Each octal digit represents three binary digits and therefore is equal to a power of 2. The rightmost digit equals to 20 (1), the next one equals to 21 (2) and the leftmost one equals to 22 (4). Write these numbers (4, 2 and 1) below the octal digits.
• Step 2: Determine which powers of two (4, 2 or 1) sum up to your octal digits. For example, if one of your octal numbers is 6, this means 4 and 2 sum up to 6 (and 1 is not used). If your octal number is 2, only 2 is used; 4 and 1 are not.
• Step 3: Write down 1 below those 4, 2 and 1’s that are used. Write down 0 below those that are not used.
• Step 4: Read 1’s and 0’s you just wrote from from left to right. You will get your binary number.

Let's apply these steps to the octal number (456)8

```Step 1:
4	5	6
421	421	421

Step 2:
4	5	6
421	421	421
(Notice the bold digits sum up to the octal value above. So the bold digits are 1 and the others are 0.)

Step 3:
4	5	6
421	421	421
100	101	110

Step 4: (456)8 = (1010011100)2
```

### Octal to Binary Conversion Examples

```Example 1: (1234)8 = (001010011100)2
1	2	3	4
421	421	421	421
421	421	421	421
001	010	011	100
```
```Example 2: (75426)8 = (111101100010110)2
7	5	4	2	6
421	421	421	421	421
111	101	100	010	110
```
```Example 3: (6574.73)8  = (110101111100.111011)2
6	5	7	4.	7	3
421	421	421	421.	421	421
110	101	111	100.	111	011
```
Binary to Octal Converter

#### Octal to Binary Conversion Chart Table

OctalBinary
100000001
200000010
300000011
400000100
500000101
600000110
700000111
1000001000
1100001001
1200001010
1300001011
1400001100
1500001101
1600001110
1700001111
2000010000
2100010001
2200010010
2300010011
2400010100
2500010101
2600010110
2700010111
3000011000
3100011001
3200011010
3300011011
3400011100
3500011101
3600011110
3700011111
4000100000
4100100001
4200100010
4300100011
4400100100
4500100101
4600100110
4700100111
5000101000
5100101001
5200101010
5300101011
5400101100
5500101101
5600101110
5700101111
6000110000
6100110001
6200110010
6300110011
6400110100
6500110101
6600110110
6700110111
7000111000
7100111001
7200111010
7300111011
7400111100
7500111101
7600111110
7700111111
10001000000
OctalBinary
10101000001
10201000010
10301000011
10401000100
10501000101
10601000110
10701000111
11001001000
11101001001
11201001010
11301001011
11401001100
11501001101
11601001110
11701001111
12001010000
12101010001
12201010010
12301010011
12401010100
12501010101
12601010110
12701010111
13001011000
13101011001
13201011010
13301011011
13401011100
13501011101
13601011110
13701011111
14001100000
14101100001
14201100010
14301100011
14401100100
14501100101
14601100110
14701100111
15001101000
15101101001
15201101010
15301101011
15401101100
15501101101
15601101110
15701101111
16001110000
16101110001
16201110010
16301110011
16401110100
16501110101
16601110110
16701110111
17001111000
17101111001
17201111010
17301111011
17401111100
17501111101
17601111110
17701111111
20010000000
OctalBinary
20110000001
20210000010
20310000011
20410000100
20510000101
20610000110
20710000111
21010001000
21110001001
21210001010
21310001011
21410001100
21510001101
21610001110
21710001111
22010010000
22110010001
22210010010
22310010011
22410010100
22510010101
22610010110
22710010111
23010011000
23110011001
23210011010
23310011011
23410011100
23510011101
23610011110
23710011111
24010100000
24110100001
24210100010
24310100011
24410100100
24510100101
24610100110
24710100111
25010101000
25110101001
25210101010
25310101011
25410101100
25510101101
25610101110
25710101111
26010110000
26110110001
26210110010
26310110011
26410110100
26510110101
26610110110
26710110111
27010111000
27110111001
27210111010
27310111011
27410111100
27510111101
27610111110
27710111111
30011000000
OctalBinary
30111000001
30211000010
30311000011
30411000100
30511000101
30611000110
30711000111
31011001000
31111001001
31211001010
31311001011
31411001100
31511001101
31611001110
31711001111
32011010000
32111010001
32211010010
32311010011
32411010100
32511010101
32611010110
32711010111
33011011000
33111011001
33211011010
33311011011
33411011100
33511011101
33611011110
33711011111
34011100000
34111100001
34211100010
34311100011
34411100100
34511100101
34611100110
34711100111
35011101000
35111101001
35211101010
35311101011
35411101100
35511101101
35611101110
35711101111
36011110000
36111110001
36211110010
36311110011
36411110100
36511110101
36611110110
36711110111
37011111000
37111111001
37211111010
37311111011
37411111100
37511111101
37611111110
37711111111

Obaid Ullah 2024-03-12 09:34:08

Daniel is right.... still it helps much

Kanokwan Apinya 2022-08-07 06:36:15

@Lessete there are no eights or nine in octal because its base(radix) is eight (if this is what you are wondering about) ;]

Vm 2022-05-22 21:03:05

Agree with Daniel. 456 octal gives 100101110 binary conversion

It is very helpful for computer studies ♥️♥️

Neven 2022-02-12 17:48:11

Thank you a lot for explaining the straightforward conversion method!

Lessette 2021-10-16 03:57:37

Thank you for your insight. I found this very helpful. I do have a question with hopes you may be you will able to help with. I noticed throughout that any digit pertaining to 8's or 9's are not found or explained. Am I correct that these are carry overs? How does this work within octal?

Daniel is right...Nonetheless the method is correct

aNITHA 2021-07-26 06:04:00

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