How to use this converter
Choose which base your number is written in (Binary, Octal, Decimal, Hex, or a Custom base), type the number, and the other bases appear instantly with copy buttons. Binary is grouped in 4-bit blocks with a bit count. Use Also show in base for any base from 2 to 36 — handy for base-5, base-12 or base-36 questions.
The four number systems
| System | Base | Digits | Decimal 13 looks like |
|---|---|---|---|
| Binary | 2 | 0, 1 | 1101 |
| Octal | 8 | 0–7 | 15 |
| Decimal | 10 | 0–9 | 13 |
| Hexadecimal | 16 | 0–9, A–F | D |
Binary → Decimal (place-value method)
Each bit is worth a power of 2. Multiply and add. For 1010:
bit: 1 0 1 0
value: 8 4 2 1
↓ ↓
1×8 + 0×4 + 1×2 + 0×1 = 10Decimal → any base (repeated division)
Divide by the base, keep the remainders, read them bottom-to-top. Example — 156 to hexadecimal:
156 ÷ 16 = 9 remainder 12 (C) 9 ÷ 16 = 0 remainder 9 (9) read up → 9C (so 156 = 9C in hex)
Binary ↔ Hex / Octal (grouping shortcut)
Group binary digits from the right: 4 bits = 1 hex digit, 3 bits = 1 octal digit. For example 1001 1110 → 9E (hex), and 10 011 110 → 236 (octal). This is why programmers write addresses and colours in hex.
Why this matters for Nepali students
Number-system conversion appears across NEB +2 Computer Science, BCA, BSc CSIT, BIT and Loksewa Computer Operator / IT exams. Practise the by-hand methods above for the written exam, and use this tool to check your answers quickly. It uses BigInt, so large values stay exact — unlike many calculators that round past ~16 digits.
Sources & notes
Standard positional number-system definitions (base 2–36, digits 0–9 then A–Z). This tool handles whole numbers (a leading minus is allowed); fractional and two’s-complement conversions may be added later. General educational information.
Working with code too? Try the JSON Formatter and Password Generator.
Frequently asked questions
How do I convert binary to decimal?
Multiply each binary digit by 2 raised to its position (starting at 0 from the right) and add them up. For 1010: (1×8) + (0×4) + (1×2) + (0×1) = 10. This tool does it instantly, but the place-value method is what you write in exams.
How do I convert decimal to binary, octal or hex?
Use repeated division: divide the decimal number by the target base, write down the remainder, and repeat with the quotient until it reaches 0. Read the remainders from bottom to top. For 156 → hex: 156 ÷ 16 = 9 r 12 (C), 9 ÷ 16 = 0 r 9, so 156 = 9C.
What is the quick way between binary and hex?
Group the binary digits into 4s from the right — each group of 4 bits is exactly one hex digit. 1001 1110 = 9E. For octal, group into 3s. This is why programmers like hex: it's a short way to write binary.
Does it handle very large numbers?
Yes, exactly. It uses BigInt, so even a 200-digit binary number converts without rounding errors. Ordinary calculators and many websites use floating-point and quietly give wrong answers past about 16 digits.
Can it convert any base, like base 5 or base 12?
Yes — pick 'Custom' for the input base, and use 'Also show in base' for the output. Any base from 2 to 36 is supported (digits 0–9 then A–Z).
Is my input sent anywhere?
No. Everything is computed in your browser — nothing is uploaded or stored.