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Binary to Octal Converter

To use binary to octal converter, type a binary value e.g. "1000" and click on the Convert button and you will get the octal value of "10" on the right side. The binary to octal conversion is explained in detail below and octal values are based on radix "8" while binary values are based on radix "2". This converter only uses unsigned values for the binary to octal conversion.

Binary to Octal Conversion:

Octal = 10

Binary Numeral System

The binary number system is a numeral system based on base-2, utilizing only two digits or bits: 0 and 1. Each digit in this system is referred to as a bit. In a binary number, every position corresponds to an increasing power of 2. Before the binary point, the rightmost bit represents 20 (ones place), the next represents 21 (twos place), followed by 22 (fours place), and so on. For fractional numbers after the binary point, bits represents the positions 2-1, 2-2 and so on.

Example:

Binary value (1101101.011)2 can be represented as:

Digit Position Power of 2 Value
1 26 (Sixty-fours place) 26 = 64 1 × 64 = 64
1 25 (Thirty-twos place) 25 = 32 1 × 32 = 32
0 24 (Sixteens place) 24 = 16 0 × 16 = 0
1 23 (Eights place) 23 = 8 1 × 8 = 8
1 22 (Fours place) 22 = 4 1 × 4 = 4
0 21 (Twos place) 21 = 2 0 × 2 = 0
1 20 (Ones place) 20 = 1 1 × 1 = 1
0 2-1 (Halves place) 2-1 = 0.5 0 × 0.5 = 0
1 2-2 (Quarters place) 2-2 = 0.25 1 × 0.25 = 0.25
1 2-3 (Eighths place) 2-3 = 0.125 1 × 0.125 = 0.125

(1101101.011)2 = (1 × 26) + (1 × 25) + (0 × 24) + (1 × 23) + (1 × 22) + (0 × 21) + (1 × 20) + (0 × 2-1) + (1 × 2-2) + (1 × 2-3) = (64 + 32 + 8 + 4 + 1 + 0.25 + 0.125) = (109.375)10 (Decimal)

Octal Numeral System

An octal number is a value expressed in the base-8 numeral system, using the digits 0 to 7. Each digit’s position represents a power of 8. For whole numbers, the rightmost digit is 80, the next is 81, then 82, and so on. For fractional parts, positions after the octal point represent decreasing powers: 8-1, 8-2, 8-3, etc.

Example:

Octal value "6756.27" can be represented as powers to the base 8:

Digit Position Power of 8 Value
6 83 place 83 = 512 6 × 512 = 3072
7 82 place 82 = 64 7 × 64 = 448
5 81 place 81 = 8 5 × 8 = 40
6 80 place 80 = 1 6 × 1 = 6
2 8-1 place 8-1 = 0.125 2 × 0.125 = 0.25
7 8-2 place 8-2 = 0.015625 7 × 0.015625 = 0.109375

(6756.27)8 = (6 × 83) + (7 × 82) + (5 × 81) + (6 × 80) + (2 × 8-1) + (7 × 8-2) = 3072 + 448 + 40 + 6 + 0.25 + 0.109375 = (3566.359375)10

How to Convert Binary to Octal

Every octal digit is represented by 3 bits. For Example 7 can be expressed in binary as "111" and 5 can be expressed as "101". Follow the following steps to convert the binary number to the octal value:

How to Convert Binary Fraction to Octal

Follow these steps to convert binary fractional value to the octal:

Binary to Octal Examples

Example 1: Convert (01011)2 to Octal value.

  • Group all the bits into 3-bit groups.
    • Group 1 Group 2
    22 21 20 22 21 20
    Position: 4 2 1 4 2 1
    Bits: 0 0 1 0 1 1
  • Multiply the position values with the bits values for all groups and add the results.
    • Group 1 Group 2
    Results: =  (4×0) + (2×0) + (1×1) =  (4×0) + (2×1) + (1×1)
    =  0 + 0 + 1 =  0 + 2 + 1
    =  (1)8 =  (3)8
  • Combine the final results of each calculation to get the final octal value:
  • (01011)2 = (13)8

    • Example 2: Convert (1011111)2 to octal value.

  • Make 3-bit groups from the MSB side.
    • Group 1 Group 2 Group 3
    22 21 20 22 21 20 22 21 20
    Position: 4 2 1 4 2 1 4 2 1
    Bits: 0 0 1 0 1 1 1 1 1
  • Multiply positions with bits and add results.
    • Group 1 Group 2 Group 3
    Results: =  (4×0) + (2×0) + (1×1) =  (4×0) + (2×1) + (1×1) =  (4×1) + (2×1) + (1×1)
    =  0 + 0 + 1 =  0 + 2 + 1 =  4 + 2 + 1
    =  (1)8 =  (3)8 =  (7)8
  • Octal value is:
  • (1011111)2 = (137)8

    • Example 3: Convert (10011101)2 to octal value.

  • Make 3-bit groups from the MSB side.
    • Group 1 Group 2 Group 3
    22 21 20 22 21 20 22 21 20
    Position: 4 2 1 4 2 1 4 2 1
    Bits: 0 1 0 0 1 1 1 0 1
  • Multiply positions with bits and add results.
    • Group 1 Group 2 Group 3
    Results: =  (4×0) + (2×1) + (1×0) =  (4×0) + (2×1) + (1×1) =  (4×1) + (2×0) + (1×1)
    =  0 + 2 + 0 =  0 + 2 + 1 =  4 + 0 + 1
    =  (2)8 =  (3)8 =  (5)8
  • Octal value is:
  • (10011101)2 = (235)8

    • Example 4: Convert (1110.10)2 to octal value.

  • While converting the binary numbers with fractional part, add zero padding on the left side for the integer part to make 3-bit groups and also after the binary point add trailing zeros to make complete 3-bit groups.
    • Group 1 Group 2 Group 3
    22 21 20 22 21 20 22 21 20
    Position: 4 2 1 4 2 1 4 2 1
    Bits: 0 0 1 1 1 0. 1 0 0
  • Multiply the position values with the bits values for all groups and add the results.
    • Group 1 Group 2 Group 3
    Results: =  (4×0) + (2×0) + (1×1) =  (4×1) + (2×1) + (1×0) =  (4×1) + (2×0) + (1×0)
    =  0 + 0 + 1 =  4 + 2 + 0 =  4 + 0 + 0
    =  (1)8 =  (6)8. =  (4)8
  • Final octal value is:
  • (1110.10)2 = (16.4)8

    • Frequently Ask Questions: Binary to Octal Conversion

    Q1: Convert signed 8-bit binary (11101010)2 value to octal?

    Since MSB = 1, it is a negative number, therefore, use 2’s complement:

    The magnitude of the value is:

    Invert bits: (00010101)2

    Add 1: 00010101 + 1 = (00010110)2 = (22)10 in decimal.

    Group the binary number into 3 bits by adding zero padding on left side: 000 010 110

    000 = 0, 010 = 2, 110 = 6, Therefore the octal value is (-26)8

    Q2: Convert (101010101010)2 to octal using 8-bit truncation?

    While doing the truncation you need to take 8 bits starting from the left side (LSB), the truncated 8-bit value is (10101010)2

    Group them into 3-bits as you can do zero padding on left side: 010 101 010.

    Convert them to the octal values 010 = 2, 101 = 6, 010 = 2, Hence octal value is: (262)8.

    Remember that the truncation results in the data loss as the 4 bits have been removed.

    Q3: Convert large binary value (11001011011110011010)2 to octal?

    First split them into 3-bit groups: 11 001 011 011 110 011 010

    Add zero padding on left side: 011 001 011 011 110 011 010

    Convert 3 bit values to octal: 011 = 3, 001 = 1, 011 = 3, 011 = 3, 110 = 6, 011 = 3, 010 = 2

    Final Octal value is: (3133632)8

    Q4: Perform a bitwise OR operation on the following two 8-bit binary numbers and express the result in octal?

    A = (10110110)2 and B = (11001101)2

                             A = 10110110

                             B = 11001101

    ---------------------------------

    A | B (Bitwise OR) = 11111111

    Group the binary number into 3-bits groups: 011 111 111

    011 = 3, 111 = 7, 111 = 7

    (11111111)2 = (377)8

    Q5: Subtract the following binary numbers and provide the result in octal?

    A = (11011010)2 and B = (10101101)2

    Convert the binary numbers to their corresponding decimal values: (11011010)2 = (218)10 and (10101101)2 = (173)10

    A - B = 218 - 173 = 45

    (45)10 = (00101101)2

    Group the bits into 3-bits: 000 101 101

    000 = 0, 101 = 5, 101 = 5, Therefore the octal value is (55)8

    Binary to Octal Conversion Table

    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

    by Wasim Khan and it was last modified on

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