Start counting positions at zero
In binary, 1010 = 1 × 2³ + 0 × 2² + 1 × 2¹ + 0 × 2⁰ = 10 in decimal.
NUMBER SYSTEMS
Base Converter●
One number. Four ways to write it. See how each conversion works.
Whole numbers only. Use a leading minus for negatives. Matching 0b, 0o and 0x prefixes are optional.
Exact integer conversion · up to 4096 bits
The same number in four bases
BinaryBase 2
OctalBase 8
DecimalBase 10
HexadecimalBase 16
Follow the conversion.
The input and explanation bases are the same. Choose a different base to follow a conversion.
Read the place values
Read positions from right to left, starting at power 0. A–F have values 10–15.
4 × 10¹ + 2 × 10⁰ = 42
The place-value expansion is hidden for inputs longer than 16 digits. All four results are still exact.
Build the new representation
Divide the magnitude repeatedly. Read the remainders from bottom to top.
Showing the first 16 divisions. More steps are needed; the full result above is exact.
Convert the magnitude, then put the minus sign back. These are signed numbers, not two’s-complement bit patterns.
A few ways to see the same number.
Open an example in the converter, then follow the conversion.
Your turn.
Ten questions using zero and positive whole numbers. Practise decimal ↔ binary, octal and hex. One scored answer per question; hints are always available.
Your chosen settings apply to the next set.
Set complete.
Your numbers, answers and scores stay in this tab. They are not uploaded or saved.
Different bases. The same place-value idea.
| Base | Value | Allowed digits |
|---|---|---|
| Binary | 2 | 0–1 |
| Octal | 8 | 0–7 |
| Decimal | 10 | 0–9 |
| Hexadecimal | 16 | 0–9, A–F |
Letters are digits too
In hexadecimal, A = 10 through F = 15. FF is 15 × 16 + 15 = 255 in decimal.
Keep the sign
−42 in decimal becomes −101010 in binary. This tool does not assume a bit width or encode two’s complement.
A base changes the notation, not the number.
Each position represents a power of its base. Binary uses powers of 2; octal uses 8; decimal uses 10; hexadecimal uses 16. Leading zeros do not change the value. Hex letters are case-insensitive.
About exact integer representation ↗Common questions
Will large numbers lose precision?
Conversions use integer arithmetic without rounding. Magnitudes up to 4096 bits are supported. Results are exact even beyond the safe range of ordinary JavaScript numbers.
Can I use prefixes such as 0xFF?
Yes. With hexadecimal selected, 0xFF is accepted; binary accepts 0b and octal accepts 0o. A prefix does not switch the selected base. Uppercase and lowercase letters both work.
What about negative numbers and two’s complement?
A minus sign is preserved in every base. This tool converts signed mathematical integers, not fixed-width machine representations. For example, −1 remains −1 rather than becoming a string of 1 bits.
Are fractions or scientific notation supported?
This version accepts whole numbers only. Decimal fractions, digit separators and scientific notation are not accepted. In hex, E is a digit, so 1E3 means 483 in decimal.
Do the practice questions repeat?
Each set contains ten distinct numerical values. New sets are generated randomly, so numbers can repeat between sets. No answer history or scores are saved.