Free binary calculator with step-by-step conversion. Convert between binary (base 2), decimal (base 10), hexadecimal (base 16), and octal (base 8) number systems instantly.
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Our binary calculator makes number base conversion easy. Whether you're a programmer, student, or working with digital electronics, instantly convert between binary, decimal, hexadecimal, and octal with detailed step-by-step explanations.
Binary is a base-2 number system that uses only two digits: 0 and 1. It's the foundation of all digital computing because electronic circuits can easily represent two states (on/off). Decimal uses 10 digits (0-9), hexadecimal uses 16 (0-9, A-F), and octal uses 8 (0-7).
Base Conversion Formula
Decimal = dₙ × bⁿ + dₙ₋₁ × bⁿ⁻¹ + ... + d₁ × b¹ + d₀ × b⁰Work with memory addresses, bit flags, and low-level data representations.
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Computers use binary because electronic circuits have two stable states: on (1) and off (0). This makes binary the most reliable way to store and process data. All higher-level numbers are built from these basic binary states.