How to convert binary to octal (example: 10011100)
The simplest way is to go through decimal (or through binary): convert binary 10011100 to decimal (156), then convert decimal to octal (234). Shortcut: each octal digit equals 3 binary digits and each hex digit equals 4 binary digits, so you can group bits directly.
Place value chart
Every digit of 10011100 (base 2) is worth its value multiplied by a power of 2. Adding the last column gives the decimal value 156.
| Digit | Place value | Contribution |
|---|---|---|
1 | 27 = 128 | 128 |
0 | 26 = 64 | 0 |
0 | 25 = 32 | 0 |
1 | 24 = 16 | 16 |
1 | 23 = 8 | 8 |
1 | 22 = 4 | 4 |
0 | 21 = 2 | 0 |
0 | 20 = 1 | 0 |
Remember: in base 8 the allowed digits are 01234567; in base 2 they are 01.
Binary to Octal table
| Binary | Octal |
|---|---|
0 | 0 |
1 | 1 |
10 | 2 |
11 | 3 |
100 | 4 |
101 | 5 |
111 | 7 |
1000 | 10 |
1010 | 12 |
1111 | 17 |
10000 | 20 |
11001 | 31 |
100000 | 40 |
110010 | 62 |
1000000 | 100 |
1100100 | 144 |
1111111 | 177 |
10000000 | 200 |
11111111 | 377 |
100000000 | 400 |
1000000000 | 1000 |
1111101000 | 1750 |
10000000000 | 2000 |
11111101010 | 3752 |
Where number systems are used
- Binary — how CPUs, memory and network packets store every value.
- Octal — Unix/Linux file permissions such as chmod 755.
- Hexadecimal — colour codes (#FF5733), MAC addresses, memory dumps and Unicode code points.
- Decimal — everyday arithmetic, prices and measurements.
About these number systems
Binary
Binary (base 2) uses only 0 and 1. Every digital device stores data in binary.
Octal
Octal (base 8) uses digits 0–7. It is used for Unix file permissions (e.g. chmod 755).
Frequently asked questions
What is 10011100 (binary) in octal?
10011100 in base 2 equals 234 in base 8.
Can it convert very large numbers?
Yes. The converter uses arbitrary-precision integers (BigInt), so large numbers convert exactly.
Is this useful for HSC ICT?
Yes. Number systems are part of the HSC ICT syllabus in Bangladesh, and the step-by-step method matches textbook solutions.