Binary to Octal
Our converter helps you easily convert binary numbers to octal format.
A binary number is expressed in the base-2 numeral system, which uses only two symbols: 0 and 1. Computers use binary numbers to perform operations because they work with bits, which can be 0 or 1.
An octal number is expressed in the base-8 numeral system, which uses eight symbols: 0 to 7. Octal numbers are often used in computing as a more compact representation of binary numbers.
Binary to Octal Converter
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Calculator
- enter a binary number, which can include a fractional part (e.g., 101.11), and it can also be negative (e.g., -1101).
Results
- the binary number converted to its octal equivalent
- the binary number converted to its decimal equivalent.
Converting a binary number to an octal number involves grouping the binary digits and then converting each group to its corresponding octal digit. Here's the general process:
Split the Binary Number
Divide the binary number into integer and fractional parts if it has a decimal point.
Group the Integer Part
Start from the rightmost digit of the integer part. Group the digits into sets of three.
If the leftmost group has fewer than three digits, add leading zeros to make it a full group of three.
Group the Fractional Part
Start from the leftmost digit of the fractional part.
Group the digits into sets of three.
If the rightmost group has fewer than three digits, add trailing zeros to make it a full group of three.
Convert Each Group to an Octal
Combine the Octal Digits
Combine the octal digits from the grouped integer part to form the integer part of the octal number.
Combine the octal digits from the grouped fractional part to form the fractional part of the octal number.
Split the Binary Number
Divide the binary number into integer and fractional parts if it has a decimal point.
Group the Integer Part
Start from the rightmost digit of the integer part. Group the digits into sets of three.
If the leftmost group has fewer than three digits, add leading zeros to make it a full group of three.
Group the Fractional Part
Start from the leftmost digit of the fractional part.
Group the digits into sets of three.
If the rightmost group has fewer than three digits, add trailing zeros to make it a full group of three.
Convert Each Group to an Octal
Combine the Octal Digits
Combine the octal digits from the grouped integer part to form the integer part of the octal number.
Combine the octal digits from the grouped fractional part to form the fractional part of the octal number.
Example Conversion
Convert binary 11101.1011 to an octal number.Split the Binary Number into Integer and Fractional Parts:
Integer part: 11101 Fractional part: 1011 To convert the integer part, group the binary digits into sets of three, starting from the right: Original integer part: 11101 Grouped as: 011 101Convert Each Group to Octal:
011 in binary is 3 in octal. 101 in binary is 5 in octal.Combine the Octal Digits:
The integer part 11101 in binary is 35 in octal.Convert the Fractional Part:
To convert the fractional part, group the binary digits into sets of three, starting from the left. Add trailing zeros if necessary to complete the last group: Original fractional part: 1011 Grouped as: 101 100 (added a trailing zero)Convert Each Group to an Octal:
101 in binary is 5 in octal. 100 in binary is 4 in octal. Combine the Octal Digits The fractional part 1011 in binary is 54 in octal.Combine the Integer and Fractional Parts:
Integer part: 35 Fractional part: 54 Octal: 35.54 The binary number 11101.1011 converted to the octal number is 35.54.