Binary Calculator
Perform high-precision binary arithmetic, bitwise logic, and base conversions.
swap_horizSystem Converter
1010 1100
172
254
AC
Arithmetic & Logic
Calculation Result
analytics0001 0110
Decimal
22
Hex
16
Octal
26
Step-by-step Solutionexpand_more
Interactive Bit-Mapper
8-BIT WORDDecimal Value
172
Hex Value
AC
Frequently Asked Questions
Arithmetic the Way the Machine Does It
The operations and what they're for
Binary math is two families — arithmetic and bitwise — with different customers:
| Operation | Example | Real use |
|---|---|---|
| Addition / subtraction | 1011 + 0110 = 10001 | Understanding overflow and carries |
| AND | 1100 AND 1010 = 1000 | Masking — keep only chosen bits |
| OR | 1100 OR 1010 = 1110 | Setting flags |
| XOR | 1100 XOR 1010 = 0110 | Toggling, checksums, simple ciphers |
| Shifts (<<, >>) | 0011 << 2 = 1100 | Fast multiply/divide by powers of 2 |
Why this matters beyond exams
Bitwise logic runs real systems: file permissions are OR-ed flags, subnet masks are AND operations (an IP AND its mask yields the network address), feature flags pack into single integers, and image alpha-blending is shift-and-mask work. Students meet binary arithmetic in CS courses; practitioners meet it the first time a permissions bug or network mask stops making sense in decimal.
Reading results comfortably
Long binary strings read best converted — the base converter renders any result in hex or decimal instantly. The networking application of AND-masks gets a dedicated treatment in the subnet calculator, and ordinary decimal arithmetic with functions lives in the scientific calculator.