# Binary to Octal Converter

To use this binary to octal conversion tool, you must type a binary value like 11011011 into the left field below and hit the Convert button. The converter will give you the octal equivalent of the given binary.

swap conversion: Octal To Binary Converter

## 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.

## 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.

## How to Convert Binary to Octal

Converting from binary to octal is very easy since octal numbers are only simplified versions of binary strings. You just need to remember that each octal digit represents three binary digits so that three binary digits will give only one octal digit. While the method is quite easier than it sounds, it’s always useful to use a binary to octal conversion chart to save time.

• Step 1: Write down the binary number and group the 0’s and 1’s in sets of three. Start doing this from the right. If the leftmost group doesn’t have enough digits to make up a set of three, add extra 0’s to make another group.
• Step 2: Write 4, 2 and 1 below each group. These are the weights that the positions carry (22,21,20).
• Step 3: Every group of three in binary will give you one digit in octal. Multiply the 4, 2 and 1’s by the digit above.
• Step 4: Add the products within each set of three. Write the sums below the groups they belong to.
• Step 5: The digits you get from the sums in each group will give you the octal number, from left to right.

Now, let’s apply these steps to, for example, the binary number (111010)2

```Step 1: 111010 has six digits and therefore can be grouped in sets of three without adding 0’s.
Think of the number as (111)(010).

Step 2: Write 4, 2 and 1 below each group.
111	010
421	421

Step 3: Multiply the 4, 2 and 1’s with the digit above.
111	010
421	421
421	020

Step 4: Add the products within each set of three.
In the first group, 4 + 2 + 1 = 7
In the second group, 0 + 2 + 0 = 2
Write these digits below the groups they belong to.
111	010
421	421
421	020
7         2

Step 5: (111010)2  = (72)8
```

### Binary to Octal Conversion Examples

Example 1: (1010001)2 = (121)8

```(1)(010)(001)
(Notice that the digits in this binary number cannot be grouped all in three.
Add two 0’s and repeat the above explained steps.)

001	010	001
421	421	421
001	020	001
1	 2	 1
```

Example 2: (10100101.01)2 = (245.2)8

```(Notice that this binary number has a decimal point.
It also cannot be automatically grouped in sets of three.
You need to add 0’s both the leftmost and the rightmost parts.)

010	100	101.	010
421	421	421.	421
020	400	401.	020
2	4	5.	2

```

Related converters:
Octal To Binary Converter

BinaryOctal
000000011
000000102
000000113
000001004
000001015
000001106
000001117
0000100010
0000100111
0000101012
0000101113
0000110014
0000110115
0000111016
0000111117
0001000020
0001000121
0001001022
0001001123
0001010024
0001010125
0001011026
0001011127
0001100030
0001100131
0001101032
0001101133
0001110034
0001110135
0001111036
0001111137
0010000040
0010000141
0010001042
0010001143
0010010044
0010010145
0010011046
0010011147
0010100050
0010100151
0010101052
0010101153
0010110054
0010110155
0010111056
0010111157
0011000060
0011000161
0011001062
0011001163
0011010064
0011010165
0011011066
0011011167
0011100070
0011100171
0011101072
0011101173
0011110074
0011110175
0011111076
0011111177
01000000100
BinaryOctal
01000001101
01000010102
01000011103
01000100104
01000101105
01000110106
01000111107
01001000110
01001001111
01001010112
01001011113
01001100114
01001101115
01001110116
01001111117
01010000120
01010001121
01010010122
01010011123
01010100124
01010101125
01010110126
01010111127
01011000130
01011001131
01011010132
01011011133
01011100134
01011101135
01011110136
01011111137
01100000140
01100001141
01100010142
01100011143
01100100144
01100101145
01100110146
01100111147
01101000150
01101001151
01101010152
01101011153
01101100154
01101101155
01101110156
01101111157
01110000160
01110001161
01110010162
01110011163
01110100164
01110101165
01110110166
01110111167
01111000170
01111001171
01111010172
01111011173
01111100174
01111101175
01111110176
01111111177
10000000200
BinaryOctal
10000001201
10000010202
10000011203
10000100204
10000101205
10000110206
10000111207
10001000210
10001001211
10001010212
10001011213
10001100214
10001101215
10001110216
10001111217
10010000220
10010001221
10010010222
10010011223
10010100224
10010101225
10010110226
10010111227
10011000230
10011001231
10011010232
10011011233
10011100234
10011101235
10011110236
10011111237
10100000240
10100001241
10100010242
10100011243
10100100244
10100101245
10100110246
10100111247
10101000250
10101001251
10101010252
10101011253
10101100254
10101101255
10101110256
10101111257
10110000260
10110001261
10110010262
10110011263
10110100264
10110101265
10110110266
10110111267
10111000270
10111001271
10111010272
10111011273
10111100274
10111101275
10111110276
10111111277
11000000300
BinaryOctal
11000001301
11000010302
11000011303
11000100304
11000101305
11000110306
11000111307
11001000310
11001001311
11001010312
11001011313
11001100314
11001101315
11001110316
11001111317
11010000320
11010001321
11010010322
11010011323
11010100324
11010101325
11010110326
11010111327
11011000330
11011001331
11011010332
11011011333
11011100334
11011101335
11011110336
11011111337
11100000340
11100001341
11100010342
11100011343
11100100344
11100101345
11100110346
11100111347
11101000350
11101001351
11101010352
11101011353
11101100354
11101101355
11101110356
11101111357
11110000360
11110001361
11110010362
11110011363
11110100364
11110101365
11110110366
11110111367
11111000370
11111001371
11111010372
11111011373
11111100374
11111101375
11111110376
11111111377