Convert Decimal to Binary
Convert decimal numbers to binary with the division steps.
Decimal to Binary Converter
Developer tool running locally in browser
What does Decimal to Binary Converter do?
Convert a decimal number to binary and follow the repeated-division working that produces it. Padding to a fixed bit width is available for when you need a byte-aligned result.
How to Use Decimal to Binary Converter
- 1Enter a decimal numberAny whole number.
- 2Choose a bit widthOptional; pads with leading zeros.
- 3Read the binaryWith the division steps below.
Key Features
- Repeated-division working shown step by step
- Optional padding to 8, 16, 32 or 64 bits
- Hexadecimal and octal shown alongside
- Exact for arbitrarily large integers
- Optional grouping into nibbles or bytes
Frequently Asked Questions
How do I convert decimal to binary by hand?
Divide by 2 repeatedly, writing down each remainder. Reading the remainders bottom to top gives the binary number. 13 gives remainders 1, 0, 1, 1 read upward, so 1101.
Why pad to a fixed width?
Because hardware and protocols work in fixed sizes. Showing 13 as 00001101 makes it clear it occupies one byte, and keeps columns aligned when comparing values.
How do I convert a decimal fraction?
Multiply the fractional part by 2 repeatedly and record the integer part each time. Note that many decimal fractions such as 0.1 never terminate in binary, which is the root of floating-point rounding surprises.
What is the binary of 255?
11111111 — eight ones, the largest value a single byte can hold. That is why 255 appears everywhere in computing, from RGB colour channels to IPv4 subnet masks.
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