Binary to Decimal Converter

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Binary to Decimal Decimal to Binary Binary to Octal Octal to Binary Binary to Hexadecimal Hexadecimal to Binary Octal to Decimal Decimal to Octal Octal to Hexadecimal Hexadecimal to Octal Decimal to Hexadecimal Hexadecimal to Decimal

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Understanding Binary and Decimal

Binary is the base-2 number system used natively by computers: every value is stored as a sequence of bits, each either 0 or 1. Digital logic gates, boolean operations, and low-level memory all operate directly in binary — it's the only number system a CPU actually understands.

Decimal is the base-10 number system used in everyday counting, built from the digits 0–9. It's the format humans read and reason about naturally, which is why programmers convert binary, octal, and hexadecimal values back to decimal whenever they need a human-readable number.

How to Convert Binary to Decimal (Step by Step)

To convert binary to decimal, multiply each bit by its positional power of 2 (starting from 1 on the right) and add the results. For example, 1010 = (1×8) + (0×4) + (1×2) + (0×1) = 10. Applying the same method to a longer value, 11001010 = 128+64+8+2 = 202.

Frequently Asked Questions

Find answers to common questions

Binary mirrors the two physical states a transistor or circuit can reliably represent: on and off, high voltage and low voltage. Every value a computer stores, from integers to text to images, is ultimately built from sequences of these two states.

No — this converter uses arbitrary-precision (BigInt) math internally, so it produces exact results even for very long binary strings or huge decimal, octal, and hexadecimal values, unlike calculators limited to 32-bit or 64-bit integers.

Free online binary to decimal converter. Convert binary numbers to decimal instantly, with support for arbitrarily large values.

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Binary to Decimal Converter