Decimal to Binary Converter: Precise Conversion with Step-by-Step Explanation
Convert any decimal number—including fractions and negatives—into binary instantly by dividing the integer part by 2 and multiplying the fraction by 2 repeatedly. Computers store data as 0 and 1 because “a single byte holds 8 bits, enabling 256 distinct values” (Computer Architecture: A Quantitative Approach, 2022).
Decimal to Binary Converter
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How to use the tool
Decimal Number – Type any real value, e.g., 45.375 or -13.3125. The sign is handled automatically.
Precision (0 – 20) – Choose how many fractional bits you need, such as 5 or 12. Blank defaults to 10.
Show Conversion Steps – Tick if you want the algorithmic breakdown for study or verification.
Press Convert to receive the binary result and, if selected, the detailed steps.
Underlying formulas
Integer part: keep dividing by 2, record remainders, then read them in reverse.
Fractional part: keep multiplying by 2, record each integer part, stop after the chosen precision.
Yes, until you exceed 9,007,199,254,740,991 (253 − 1) [MDN, link].
Does the tool show two’s-complement?
No. It displays sign-magnitude; use a dedicated two’s-complement calculator for bitwise work (Intel Developer Manual, 2022).
How do I shorten long fractional outputs?
Reduce the precision field; fewer iterations mean a shorter, still correct, binary string (Knuth, 2015).
Is negative zero possible?
The output never shows “-0”. A zero input returns exactly 0 as defined in IEEE 754 (IEEE Std 754-2019).
Who uses binary fractions?
Digital signal processors store fixed-point numbers where each fractional bit equals rac1{2}n of scale (TI TMS320 Datasheet, 2021).
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