Binary to Octal Converter

Enter a binary number below to convert it to octal.

Octal Number:

Steps to Convert to Octal

Learn how we calculated this below

How to Convert Binary to Octal

The binary number system is a base 2 number system since it only uses the digits 0 and 1. Octal is a base 8 number system since it uses eight digits: 0, 1, 2, 3, 4, 5, 6, and 7.

Binary and octal numbers are often used in computing applications, so it’s fairly common to need to convert from one to the other.

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. Since these are cleanly divisible into base 16 numbers, the hexadecimal system is much more common.

You can convert from binary to octal in just a few steps.

Step One: Split into Groups of Three Digits

The first step is to break the binary number into groups of three digits, starting from the right to the left. The reason for this is that a group of three base 2 numbers, or 2³ is equal to 8, which is evenly divisible into the base 8 number system.

For example, the binary number 1110001111011 can be broken into the following groups:

1110001111011
(1)(110)(001)(111)(011)

It is okay if the first group does not have three digits. You can also add additional zeros to precede the digits in the first group so that there are three digits.

Step Two: Convert Each Binary Group to an Octal Digit

At this point, each group of three binary digits can be converted to an octal digit using the following table.

3-bit Binary Words to Octal Values

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

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

Applying this to the binary number above that we split into groups of three digits:

1₂ = 1₈
110₂ = 4 + 2 + 0 = 6₈
001₂ = 0 + 0 + 1 = 1₈
111₂ = 4 + 2 + 1 = 7₈
011₂ = 0 + 2 + 1 = 3₈

So, 1110001111011₂ in binary is equal to 16173₈ in octal.

You can also use a tool like our binary calculator to convert to decimal or hex.

Binary to Octal Conversion Table

The table below shows binary numbers and the equivalent octal number values.

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

Binary to Octal Converter

Have a Question or Feedback?