Decimal to Binary Converter

Q: Can I convert many decimal numbers at once?

Yes. Put one number per line and every line is converted, with the results lined up against the input. A line that is not a valid decimal number is left blank and reported by line number, so one typo does not stop the rest.

Q: How do you convert decimal to binary by hand?

Divide by 2 repeatedly and write down the remainders; the binary number is the remainders read from last to first. For 13: 13→6 r1, 6→3 r0, 3→1 r1, 1→0 r1, giving 1101.

Q: How is a negative number written in binary?

Mathematically with a minus sign, but computers use two's complement: invert every bit of the positive value and add one. −5 at 8 bits is the inverse of 00000101, which is 11111010, plus one: 11111011. The tool shows this pattern for you.

Q: How many bits does a number need?

The number of binary digits in its value: 255 needs 8, 256 needs 9. The tool reports the bit count and the smallest standard integer width — 8, 16, 32 or 64 bits — that holds it.

Convert decimal numbers to binary instantly — padded to whole bytes if you like — with two's complement for negative numbers.

Decimal

Binary

Group digits Add 0x / 0b / 0o prefix Uppercase hex Pad to whole bytes

What It Does

This converter writes a decimal number in binary. It works for any size — the arithmetic is exact, not floating point — and can pad the result to whole bytes and group it into nibbles so it reads like a memory dump. For a negative number it shows the minus-sign form and, alongside it, the two's-complement bit pattern a computer actually stores.

When to Use It

You are setting bit flags and want to see which bits a decimal constant turns on.
You are learning or teaching how numbers are represented in binary.
You need the stored bit pattern of a negative integer for a low-level protocol or a test.
You have a list of decimal IDs or codes to convert in one go.

Worked Examples

42

101010. Tick Pad to whole bytes to see 00101010, the way it sits in an 8-bit register.

-5

Written as −101, but stored as the 8-bit two's-complement pattern 1111 1011.

1024

10000000000 — a single 1 followed by ten zeros, because 1024 is 2^10. Powers of two are always a lone 1 in binary.

Features

Converts as you type

Bulk conversion one number per line

Exact for numbers of any size

Digit grouping and 0x/0b/0o prefixes

Swap direction in one click

Explains bit width and two's complement

How to Use

1. Type or paste a decimal number — or a list, one per line. 2. The binary value appears alongside, line for line. 3. Use the options to group digits or add a prefix, and the swap button to convert the other way.

Common Mistakes

Converting a number through a JavaScript Number. Above 9,007,199,254,740,991 it silently rounds, so the last digits come out wrong. This tool uses BigInt and stays exact at any size.
Forgetting that the same digits mean different values in different bases. 10 is ten in decimal, two in binary, eight in octal and sixteen in hex — always label which base a value is in.
Treating a minus sign as how a computer stores a negative number. Hardware uses two's complement, so a negative value's bit pattern looks nothing like its positive counterpart.

Frequently Asked Questions

Can I convert many decimal numbers at once?

How do you convert decimal to binary by hand?

How is a negative number written in binary?

How many bits does a number need?

Conversion runs in your browser with exact integer arithmetic. Nothing is uploaded.