Complete guide
Binary calculator with exact integer arithmetic and conversion
Calculate two binary integers or convert in either direction. Calculator24 returns binary, decimal and hexadecimal forms together so every answer can be cross-checked.
How binary place value works
Binary uses only digits 0 and 1. Reading right to left, positions represent 2⁰, 2¹, 2² and so on.
Exact arithmetic modes
Addition, subtraction and multiplication return signed whole integers. Division reports quotient and remainder rather than silently discarding the leftover.
Binary to decimal
Multiply each 1 bit by its power of two and add those place values.
10111₂=1×2⁴+0×2³+1×2²+1×2¹+1×2⁰=23Decimal to binary
Repeated division by two produces remainder bits. Reading remainders from last to first gives the binary representation.
Worked addition example
10101₂ is 21 and 111₂ is 7. Their sum 28 is 11100₂.
Signed and fixed-width limits
A leading minus sign represents a mathematical negative integer, not a fixed-width two's-complement bit pattern. Hardware overflow and word size require an explicit separate model.
Binary place values
| Power | Binary place | Decimal value |
|---|---|---|
| 2⁰ | 1 | 1 |
| 2¹ | 10 | 2 |
| 2² | 100 | 4 |
| 2³ | 1000 | 8 |
| 2⁴ | 10000 | 16 |
Frequently asked questions
Can I enter negative binary integers?
Yes, with one leading minus sign.
Does division show a remainder?
Yes. It reports exact integer quotient and remainder.
Are results limited to 32 bits?
No. BigInt keeps exact integers up to the page's 256-digit input limit.
Does this support binary fractions?
No. Inputs are whole integers.
What is 1010 in decimal?
It is 10.
Is a negative result two's complement?
No. It is displayed with a minus sign.
What to keep in mind
Whole signed integers only, up to 256 binary digits. Division returns integer quotient and remainder; fractional binary values and fixed-width overflow are outside scope.
Results display up to 8 decimal places; exported numbers preserve calculation precision. This is a calculation summary, not an official certificate.