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Conversion of binary to octal

Updated: 8/9/2023
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11y ago

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Binary is a base 2 number system, while octal is base 8. This happens to make conversion between binary and octal fairly trivial, although more complex than conversion to hexadecimal. To convert to octal from binary, take each three bits, starting from the least significant bit, and convert them to their octal equivalent.

Examples:

25510 = 111111112 = 11 111 111 = 3778

17410 = 101011102 = 10 101 110 = 2568

You can repeat this process for as many bits as you need. A 24-bit number should translate into 8 octal numbers, for reference.

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12y ago
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13y ago

The octal number system consists of the digits 0 - 7, whose binary equivalents are as follows -

Octal Binary

0 000

1 001

2 010

3 011

4 100

5 101

6 110

7 111

For converting any octal number to binary, simply take each of its digits and replace it by its binary equivalent, irrespective of its position. For example,

(76.53) in octal is equivalent to (111110.101011) in binary.

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12y ago

i think we can use 421 code to convert it...

for the question given let us consider digits after decimal point...

first group the digits in such a way that each group has three digits... grouping must be done from the rightmost digit......then apply 421 code...likewise same procedure is followed for digits b4 the decimal points...

Hence the answer is 415.151

i think it will go like this

10 001 101.011 010 01

grouping before decimal FM right and after FM left and using 8421 code

it is : 215.322

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11y ago

Working from right to left, split the binary digits into groups of three bits. Each group is treated as a separate binary number. Thus for each group, bit-0 (the least-significant bit) represents the decimal value 1, bit-1 the decimal value 2 and bit-2 (the most-significant bit) the decimal value 4. Adding all the set bits together in each group yields an octal digit in the range 0 to 7 inclusive.

For example:

1001101011 (decimal 619) can be split into the following groups of three bits (with (00) padding in the first group):

(00)1 = 1

001 = 1

101 = 4+1 = 5

011 = 2+1 = 3

Thus 1001101011 binary is 1153 octal.

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16y ago

Starting from the right divide the binary number up in 3 bit sections, then convert each 3 bit section into its decimal equivalent.
Example: 101001110111012 = 10|100|111|011|101 =247358

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14y ago

It's easy to convert binary to octal. Each 3 bit group of a binary number convert to an octal value. We work right to left.

1 101 001 111 011 = 15173

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How do you write a C program to convert a binary value to its octal equivalent?

To convert from binary to octal, bitwise AND the binary value with 0x8 (00000111 in binary) and push the value onto a stack. Right-shift (>>) the binary value by 3 bits and repeat until the binary value is zero. Pop the stack to build the left-to-right digits of the octal value. Using 10110100 as an example: 10110100 & 00000111 = 00000100 10110100 >> 3 = 00010110 00010110 & 00000111 = 00000110 00010110 >> 3 = 00000010 00000010 & 00000111 = 00000010 00000010 >> 3 = 00000000 Popping the values in order reveals 00000010, 00000110 and 00000100 (decimal 2, 6 and 4 respectively). Thus 10110100 binary is 0264 octal.


What is conversion of 125 into binary?

1111101 If you use windows calculator click on view and select scientific. Then you too will be able to easily convert between numbering systems. Alternately you could learn the different numbering systems (binary, decimal, octal and hexadecimal) as this proves most useful when programming.


How do you convert octal digits into three binary digits?

C++ does not support octal encoding within source code (only decimal and hexadecimal are supported), so the octal must be represented with a string. The binary output must also be a string. Every octal digit represents three bits of binary, thus the binary output string will always be three times the length of the octal input string. The loop will begin with the octal character at index 0 and work through each character from left to right. On each iteration, the binary output string will be appended with a 3-character string, as follows: octal = binary "0" = "000" "1" = "001" "2" = "010" "3" = "011" "4" = "100" "5" = "101" "6" = "110" "7" = "111" Thus octal input "437" will begin with the "4" producing an output of "100". On the next iteration, "3" will append "011" to produce "100011". On the final iteration, "7" will append "111" to produce "100011111".


How convert octal to binary?

If necessary, pad the value with zeroes so the number of bits is an exact multiple of 3. Then divide the binary value into groups of 3 bits. Convert each group to its corresponding octal digit as follows: Bin = Oct 000 = 0 001 = 1 010 = 2 011 = 3 100 = 4 101 = 5 110 = 6 111 = 7 Example 1: 16-bit value: 1011101101100011 3-bit groupings: (00)1 011 101 101 100 011 Octal digits: 1 3 5 4 3 Octal value: 13543 Example 2: 24-bit value: 010111011010010101011010 3-bit groupings: 010 111 011 010 010 101 011 010 Octal digits: 2 7 3 2 2 5 3 2 Octal value: 27322532


Show that 8's complement octal and 2's complement binary are exactly equivalent.?

trivial.

Related questions

How do you convert octal to binary with 2 decimal nos?

The conversion of octal number to binary can be obtained by using two methods. First, it can be converted into decimal and then obtained decimal is converted into binary. In the second method


Example of binary to octal conversion?

01012 = 58 10002 = 108 10102 = 128 11112 = 178


Convert the hexadecimal number ABCDEF to octal and binary?

Octal = 52746757 Binary = 101010111100110111101111


How do you convert 1470 octal to binary?

1470 octal = 001 100 111 000 binary


Convert the decimal numbers 1987 to binary then to octal?

In binary this number is equivalent to 11111000011 while in octal it is 3703


Change from Binary number 110101001 to octal?

110101001 = 651 octal


What is the binary equivalent of the octal number 76?

Octal 76 = 111110


Convert the hexadecimal number 221122 into binary octal and decimal?

221122: Binary = 1000100001000100100010 Octal = 10410442 Decimal = 2232610


Convert octal number 889 to binary?

Don't. 889 is not an octal number.


Convert binary numbers to octal numbers 1111111010?

1111111010 = octal 1772


What octal value is equal to binary number 001 110 101?

Binary number 1110101 equates to octal number 165.


How will you convert octal to hexadecimal?

Each octal digit is equivalent to three binary digits; each hexadecimal digit is equal to four binary digits. I think the best way to do this conversion is to convert each octal digit into the binary equivalent (3 digits in each case - don't omit the zeros on the left), then convert the binary to hexadecimal by grouping four binary digits at a time (starting from the right). Note that nowadays, most scientific calculators - including the calculator that comes included in Windows - have the ability to do this sort of conversion. If you want to practice doing it yourself, you can still use the Windows calculator to check your calculations.