Dezimal-zu-Binär-Umrechner

Q: What input formats are supported?

We accept integers with an optional sign. Before calculating we strip spaces and underscores so only digits remain; fractional parts and exponents are not supported.

Q: How does the Auto bit-width mode work?

We calculate the minimum bits for the magnitude and add one extra bit when the number is negative. This prevents truncation; choose a manual width if you prefer fixed padding.

Q: How is two's complement calculated?

With bit-width n , we take the magnitude in binary, pad it to n bits, flip every bit, and add 1. If the value does not fit in n bits, you'll be asked to widen the width.

Q: What is the limit of the step-by-step table?

To keep the view clear, we show the division breakdown up to 2048 bits. Above that size we still compute with BigInt, but hide the detailed table.

Q: Can I group bits, copy, and reuse the result?

Yes. You can group bits into 4- or 8-bit blocks, copy each output with its dedicated button, and jump to the other calculators using the shortcuts above to keep working.

Wandle Dezimal in Binär mit BigInt um, mit konfigurierbarem Padding und Zweierkomplement. Sieh die Division-Schritte und erhalte Hex/Oktal.

Decimal to Binary Calculator Online (Step-by-Step)

Convert decimal to binary with BigInt, add custom padding, get hex/octal equivalents, and review the repeated division steps. Everything is stacked vertically for a distraction-free flow.

Binary → Decimal Decimal → Binary Binary → Hexadecimal Binary → Octal Binary → ASCII/Text

Decimal (integer, sign allowed)

Binary

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Main result

Grouped binary

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Signed binary (two's complement)

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Hex with padding

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Octal

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Derived from the magnitude or two's complement pattern

Automatic steps: repeated division by 2

Dividend Quotient Remainder Step

Dividend	Quotient	Remainder	Step

How to convert decimal to binary

The manual method divides by 2 repeatedly and stores the remainders; they are read in reverse order. For negative numbers, apply two's complement with the chosen bit width.

Clean the input. Remove spaces, underscores, and duplicate signs; keep only digits and an optional leading sign.
Take the magnitude. Work with the absolute value to build the unsigned binary.
Divide by 2. Record the quotient and remainder (0 or 1) on each step.
Iterate. Use the new quotient as the dividend until it reaches 0.
Read backwards. The unsigned binary is the sequence of remainders from last to first.
Two's complement. If the decimal is negative and you pick a bit-width n, pad the magnitude to n bits, flip all bits, and add 1. If the magnitude does not fit in n bits, you'll be prompted to increase the width.

Positive example (10973): successive divisions produce remainders 1 0 1 0 1 0 1 0 0 1 0 1 1 0 1; in reverse order they form 101010010110101.

Negative example (-25) with 8 bits: the magnitude is 11001, padded to 00011001, inverted to 11100110, and adding 1 gives 11100111.

0 → 0 1 → 1 5 → 101 13 → 1101 42 → 101010 255 → 1111 1111