Binary Calculator for Practice and Tests
Check your decimal ↔ binary conversions and base-2 calculations. Ideal for computing, physics or binary system exercises — use the tool to verify, then ask your question on Math AI for a step-by-step explanation.
Binary calculation – Addition, Subtraction, Multiplication or Division
Result
Binary value:
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Decimal value:
Convert Binary to Decimal
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Convert Decimal to Binary
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Quick Guide to Binary
Binary is a base-2 number system used in computing. It uses only 0 and 1. Each position corresponds to a power of 2 (2⁰, 2¹, 2² …).
This calculator serves for quick conversion and verification of base-2 calculations.
Conversion Methods
- Decimal → Binary: repeated division by 2, read remainders from bottom to top.
- Binary → Decimal: sum of bits × 2ⁿ according to position.
- Control: The binary result can be converted back to decimal.
Examples
42 in Binary: 42 ÷ 2 → 21 R.0 ; 21 ÷ 2 → 10 R.1 ; 10 ÷ 2 → 5 R.0 ; 5 ÷ 2 → 2 R.1 ; 2 ÷ 2 → 1 R.0 ; 1 ÷ 2 → 0 R.1 → 101010₂.
1010₂ in Decimal: 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 10.
Addition: 1101₂ + 1011₂ = 11000₂ (carry like base 10).
Applications in Computing
- Representation of data in electronic circuits.
- Color coding, memory addresses, bit masks.
- Understanding powers of 2 (bytes, kilobytes, etc.).
FAQ
- Why Binary? Two states (0/1) are reliable in electronics.
- Common errors: forgetting the positions (2⁰, 2¹, 2² …).
- Need an explanation? The Math AI assistant can explain the method.