# Binary to decimal calculator with steps

Looking to convert to binary floating-point? Try my floating-point converter. Looking to calculate with binary numbers? Try my binary calculator. Looking to convert numbers between arbitrary bases? Try my base converter. This is a decimal to binary and binary to decimal converter. Conversion is implemented with arbitrary-precision arithmeticwhich gives the converter its ability to convert numbers bigger than those that can fit in standard computer word sizes binary to decimal calculator with steps 32 or 64 bits.

Besides the converted result, the number of digits in both the original and converted numbers is displayed. For example, when converting decimal This means that the decimal input has 2 digits in its integer part and 3 digits in its fractional part, and binary to decimal calculator with steps binary output has 6 digits in its integer part and 3 digits in its fractional part.

Fractional decimal values that are dyadic convert to finite fractional binary values and are displayed in full precision. Fractional decimal values that **binary to decimal calculator with steps** non-dyadic convert to infinite repeating fractional binary values, which are truncated — not rounded — to the specified number of bits. The converter is set up so that you can explore properties of decimal to binary and binary to decimal conversion. A decimal integer or dyadic fractional value converted to binary and then back to decimal matches the original decimal value; a non-dyadic value converts back only to an approximation of its original decimal value.

Increasing the number of bits of precision will make the converted number closer to the original. You can study how the number of digits differs between the decimal and binary representations of a number. Large binary integers have about log 2 10or approximately 3. Dyadic decimal fractions have the same number of digits as their binary equivalents.

Non-dyadic decimal values, as already noted, have infinite binary equivalents. This converter also converts between bases other than binary and decimal.

Skip to content Decimal to Binary Enter a decimal number e. Truncate infinite binary fractions to bits.