Binary Calculator
Convert a decimal number to binary, or a binary number back to decimal, instantly.
How Binary Works
Each position in a binary number represents a power of 2, the same way each position in a decimal number represents a power of 10.
Worked example
Convert 42 to binary.
42 = 32 + 8 + 2 = 2⁵ + 2³ + 2¹
42 in binary = 101010
Frequently Asked Questions
What is binary?
Binary is a number system that uses only two digits, 0 and 1, instead of the ten digits (0-9) used in the everyday decimal system. It's the language computers use internally, since a digital circuit's two states (on and off) map directly onto 0 and 1.
How do you convert decimal to binary?
Repeatedly divide the number by 2, recording the remainder at each step. Reading the remainders from last to first gives the binary representation.
How do you convert binary to decimal?
Each binary digit represents a power of 2 based on its position, starting from 2⁰ on the right. Multiply each digit by its place value and add the results together.
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