Convert octal to binary as you type, with every step shown. This free online converter gives exact results for numbers of any size, and nothing you type leaves your browser.
1 Enter your value
From
To
0x
Examples
2 Your answer
Decimal
dec
Show in other bases
Tap any value to copy it.
See the working
Guide
How it works
Three steps, whether you are reading a memory address, a bit flag or a byte value.
1
Choose what to convert
Pick what you have and what you want: decimal, hexadecimal, binary or octal.
2
Type or paste a value
Write it however you like: 65,535, 0xFF, FFh, with commas, spaces or underscores.
3
Read the answer
It appears as you type, in every other base, with the working shown.
The formulas
A digit's value depends on its position. Every answer here uses one of these rules:
Octal to binary
each octal digit = 3 binary bits
0o643 is 6 → 110, 4 → 100, 3 → 011, so 0o643 is 110 100 011.
Binary to octal
group the bits in threes from the right
0b110100011 → 110 100 011 → 6, 4, 3, so 0b110100011 is 0o643.
Octal to decimal
decimal = Σ digit × 8position
0o643 is 6 × 64 + 4 × 8 + 3 × 1 = 419, so the answer checks out.
Decimal to hexadecimal digit chart
The decimal values 0 to 15 are the single hexadecimal digits 0 to F. Click one to add it to the converter.
All conversions
Decimal, hexadecimal, binary and octal converter
One free tool for every direction. Use it as a decimal to hexadecimal converter, convert decimal to binary or octal, or work backwards as a hexadecimal to decimal converter that turns 0x to decimal values. It also converts hexadecimal to binary, binary to hexadecimal and octal to decimal, so it works as a full number base converter and hexadecimal calculator. Pick a conversion to start.
Each octal digit stands for exactly 3 binary bits. Replace every octal digit with its 3-bit group.
Join the groups together and drop any leading zeros.
Worked example
0o643 → 110 100 011
= 0b110100011
Octal to Binary conversion table
Use this octal to binary table as a quick octal to binary chart for common values, from 0 to 65,535.
Octal
Binary
0
0
1
1
2
10
3
11
4
100
5
101
6
110
7
111
10
1000
11
1001
12
1010
13
1011
14
1100
15
1101
16
1110
17
1111
20
1 0000
40
10 0000
100
100 0000
144
110 0100
177
111 1111
200
1000 0000
377
1111 1111
400
1 0000 0000
1000
10 0000 0000
1750
11 1110 1000
2000
100 0000 0000
10000
1 0000 0000 0000
177777
1111 1111 1111 1111
Help
Questions
Quick answers to what people most often ask about hexadecimal, decimal and binary.
01How do I convert octal to binary?
Each octal digit stands for exactly 3 binary bits. Replace every octal digit with its 3-bit group. Join the groups together and drop any leading zeros.
02What is 377 in binary?
0o377 in octal is 0b11111111 in binary (255 in decimal). Type 377 into the converter above to see every step.
03What is 2000 in binary?
0o2000 in octal is 0b10000000000 in binary (1,024 in decimal).
04What is 10 in binary?
0o10 in octal is 0b1000 in binary (8 in decimal).
05What is 755 in binary?
0o755 in octal is 0b111101101 in binary (493 in decimal). It is the 755 in chmod 755 (rwxr-xr-x).
06What is 777 in binary?
0o777 in octal is 0b111111111 in binary (511 in decimal). It is the 777 in chmod 777: read, write and execute for everyone.
07Why is one octal digit exactly three binary bits?
Because 8 = 2³. Three bits can hold 8 different values, 000 to 111, which is exactly the range of one octal digit, 0 to 7. So 0o777 is 111 111 111 in binary.
08How do I convert octal to binary in Excel?
Use the OCT2BIN function: =OCT2BIN("377") returns 11111111. It works the same way in Google Sheets. These functions only handle up to 10 input characters, and the binary ones only −512 to 511, so use this converter for larger numbers.
09How do I convert octal to binary in Python or JavaScript?
In Python, bin(int('377', 8)) returns '0b11111111'. In JavaScript, parseInt('377', 8).toString(2) returns '11111111'. Python handles any size; in JavaScript use BigInt for numbers above 2⁵³.
10Does the converter use two’s complement for negative numbers?
No. It keeps the minus sign, so −255 is −0xFF, −0b11111111 and −0o377. Computers usually store negative numbers in two’s complement, where the pattern depends on the width: −1 is 1111 1111 (0xFF) in 8 bits and 0xFFFF in 16 bits. To read a signed value whose top bit is set, subtract 2ⁿ: 0xFF as a signed 8-bit number is 255 − 256 = −1.
11Can I convert octal numbers with a fractional part?
The converter works with whole numbers. By hand, convert the fractional part by multiplying it by the target base again and again and keeping the whole-number part each time. For example, 0.5 × 16 = 8, so 0.5 is 0x0.8 in hexadecimal, 0b0.1 in binary and 0o0.4 in octal.
12How many bits are in a byte?
Eight. A byte holds 0 to 255, which is 0000 0000 to 1111 1111 in binary, 0x00 to 0xFF in hexadecimal and 0o000 to 0o377 in octal.
13Is there a limit to how big a octal number can be?
No. The converter uses exact whole-number arithmetic, so 64-bit, 128-bit and longer octal values convert to binary with every digit correct, with no rounding.
14What does “oct to bin” mean?
“oct to bin” is short for octal to binary, which means going from base 8 to base 2: a number written in base 8 is rewritten in base 2. For example, 0o377 becomes 0b11111111.
15Does this octal to binary calculator show the working?
Yes. It converts octal to binary with steps: open “See the working” under the answer to see each digit multiplied by its power of 8, then the result written in binary. Every answer is also shown in decimal, hexadecimal, binary and octal at once.
16Is this octal to binary converter free?
Yes. It is free with no sign-up, works online on phones, tablets and computers, and every octal to binary conversion runs in your browser, so nothing you type is sent anywhere.