Binary Calculator
Adjust the inputs below. Results update as you type.
How it works
Binary arithmetic follows the same rules as decimal but with only digits 0 and 1 and carries at 2 instead of 10. Two's complement represents negative numbers in most computer systems. Enter numbers in any base using the prefix (0b for binary, 0x for hex) or select the base from the dropdown. Useful for computer science coursework and low-level programming.
Input guidance
- Check units and decimal placement before running calculations.
- For percentage and ratio tasks, define the baseline value clearly.
- Use rounded output carefully and keep full precision for intermediate steps.
The formula
Binary is base-2, using only 0 and 1. Each position is a power of two. Convert to decimal by summing position values; arithmetic works like decimal but carries at 2.
Worked example
Binary 1011 = 1×8 + 0×4 + 1×2 + 1×1 = 11 in decimal.
More examples to test
- Baseline example: solve with clean numbers first to verify formula direction.
- Edge-case example: test near-zero or boundary values to avoid interpretation errors.
How to interpret results
Use outputs as quick checks, then verify with step-by-step work for graded or high-stakes use.
When this can be inaccurate
Errors usually come from unit mismatch, wrong baseline assumptions, or rounding too early in multistep problems.
Change history
- July 2026: Quality-reviewed for publication with formula checks and explanatory copy updates.
Site-wide corrections also appear on the corrections log.
Build math and logic skills with guided lessons
Educational platform recommendation.
Frequently asked questions
How do I convert binary to decimal?+
Multiply each digit by its power of two (right to left: 1, 2, 4, 8…) and add. 1101 = 8+4+0+1 = 13.
Why do computers use binary?+
Electronic circuits have two stable states (on/off), which map naturally to 1 and 0, making binary the foundation of digital computing.
How does binary addition work?+
Like decimal but you carry when a column reaches 2. 1 + 1 = 10 in binary (zero, carry one).
Why do my classroom and calculator results differ?+
Differences usually come from rounding conventions, order-of-operations handling, or different baseline assumptions.
What is the safest way to validate an answer?+
Recompute with units shown and check against a second method or manual arithmetic for critical problems.