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
A second example
Convert the binary number 110101 to decimal.
1(32) + 1(16) + 0(8) + 1(4) + 0(2) + 1(1) = 32 + 16 + 4 + 1
110101 in decimal = 53
Keep going
- Binary and Roman numerals are both alternatives to base-10 notation; the Roman numeral converter runs that same kind of number through a different symbol system. Roman Numerals Calculator
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.
What is a byte, in binary?
A byte is 8 binary digits (bits). With 8 bits you can represent 2⁸ = 256 distinct values, typically counted 0 through 255 — the range used for a single color channel in RGB, for example.
What's a common mistake when reading binary?
Reading the digits left to right as if they were decimal place values. The rightmost digit is always the 2⁰ (ones) place, and place value doubles moving left — so 101 means 1(4) + 0(2) + 1(1) = 5, not "one hundred one."
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