Binary calculator with exact integer arithmetic and conversion
Calculate two binary integers or convert in either direction. HitEquals returns binary, decimal and hexadecimal forms together so every answer can be cross-checked.
Inputs used by this calculator
Binary Calculator uses the fields below. The starting values reproduce the page example; replace them with values from the same units and time period before using the result.
| Input | Starting example | Accepted value | How it is used |
|---|---|---|---|
| Operation mode | Binary arithmetic | Binary arithmetic · Binary to decimal · Decimal to binary | Chooses which Binary Calculator method or unknown the engine evaluates. |
| First binary integer | 10101 | Text in the format shown | Supplies the first binary integer quantity used by the published equation or result breakdown. |
| Operator | Add | Add · Subtract · Multiply · Divide | Selects the unit or conversion path used by Binary Calculator. |
| Second binary integer | 111 | Text in the format shown | Supplies the second binary integer quantity used by the published equation or result breakdown. |
| Decimal integer | 42 | Text in the format shown | Supplies the decimal integer quantity used by the published equation or result breakdown. |
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.
Reading binary without a converter
Write powers of two from right to left beginning with 1. Add only positions containing a 1. For 10101₂, the included places are 16, 4 and 1, which sum to 21.
Binary arithmetic versus computer storage
This page performs exact mathematical integer arithmetic. Computer systems also choose a fixed bit width, signed representation and overflow behavior. Those implementation choices can change how a negative bit pattern is interpreted even when the underlying integer operation is familiar.
Binary place values
| Power | Binary place | Decimal value |
|---|---|---|
| 2⁰ | 1 | 1 |
| 2¹ | 10 | 2 |
| 2² | 100 | 4 |
| 2³ | 1000 | 8 |
| 2⁴ | 10000 | 16 |
Four-bit binary reference
| Binary | Decimal | Hex |
|---|---|---|
| 0000 | 0 | 0 |
| 0001 | 1 | 1 |
| 0010 | 2 | 2 |
| 0100 | 4 | 4 |
| 1000 | 8 | 8 |
| 1111 | 15 | F |
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.
Do leading zeros change a binary integer?
No for mathematical value, although they can indicate a chosen storage width.
Why does one hexadecimal digit equal four bits?
Four binary positions represent 16 combinations, matching one base-16 digit.
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 are rounded for display in US format, with money in dollars and cents; CSV exports keep full calculation precision. This is a calculation summary, not an official certificate.