Decimal to Binary Calculator — With Steps
Binary Value
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Division Steps
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Hexadecimal
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Octal
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How to Convert Decimal to Binary
To convert a decimal number to binary, repeatedly divide the number by 2 and record the remainders. The binary representation is the sequence of remainders read from bottom to top (last remainder first).
For example, 214 to binary: 214/2=107 r0, 107/2=53 r1, 53/2=26 r1, 26/2=13 r0, 13/2=6 r1, 6/2=3 r0, 3/2=1 r1, 1/2=0 r1. Reading remainders bottom-up: 11010110.
This calculator also shows the hexadecimal (base-16) and octal (base-8) representations, which are commonly used in programming and computer science as shorthand for binary values.
Frequently Asked Questions
Why is hexadecimal used instead of binary?
Hexadecimal is a compact representation where each hex digit represents exactly 4 binary digits. This makes it much easier to read long binary strings. For example, binary 11111111 = FF in hex.
What is octal?
Octal is base-8, using digits 0-7. Each octal digit represents 3 binary digits. It was historically used in computing (e.g., Unix file permissions use octal notation).
Can this convert negative numbers?
This calculator handles non-negative integers. Negative numbers in binary use two's complement representation, which involves flipping bits and adding 1 to the positive binary form.