Decimal to Binary Converter
Convert decimal numbers to standard binary notation, two's complement signed formats, and IEEE-754 32-bit floating point structures.
Binary Conversion Step-by-Step Proof
Powers of 2 and Binary Bit Reference
Standard byte ranges and binary bit weights.
| Decimal | Binary Form | Power / Weight | Action |
|---|---|---|---|
| 0 | 0000 0000 | 2⁰ = 1 | |
| 1 | 0000 0001 | 2⁰ | |
| 2 | 0000 0010 | 2¹ | |
| 4 | 0000 0100 | 2² | |
| 8 | 0000 1000 | 2³ | |
| 16 | 0001 0000 | 2⁴ | |
| 32 | 0010 0000 | 2⁵ | |
| 64 | 0100 0000 | 2⁶ | |
| 128 | 1000 0000 | 2⁷ | |
| 255 | 1111 1111 | 8-bit Max (2⁸ - 1) | |
| 256 | 0001 0000 0000 | 2⁸ | |
| 65535 | 1111 1111 1111 1111 | 16-bit Max (2¹⁶ - 1) |
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Frequently Asked Questions
Everything you need to know about decimal conversions, accuracy, and formulas.
01How do you convert decimal to binary manually?▼
To convert an integer decimal to binary: repeatedly divide the number by 2 and record the remainders (0 or 1) in reverse order. For fractional decimals (e.g. 0.625), repeatedly multiply the fraction by 2 and record the integer parts until the fractional part reaches zero.
02What is IEEE 754 32-bit Floating Point representation?▼
IEEE 754 single precision float uses 32 bits to store real numbers: 1 bit for the sign (0 for positive, 1 for negative), 8 bits for the biased exponent (bias of 127), and 23 bits for the mantissa (significand fraction). This is how computers natively store fractional decimal values.
03How does Two's Complement represent negative binary numbers?▼
Two's complement is the standard system for representing signed integers. To convert a positive number into negative: invert all the bits (one's complement) and add 1. For example, +5 (00000101) becomes -5 (11111011).