IEEE 754 Converter

You can either convert a number by choosing its binary representation in the button-bar, the other fields will be updated immediately. Or you can enter a binary number, a hexnumber or the decimal representation into the corresponding textfield and press return to update the other fields. To make it easier to spot eventual rounding errors, the selected float number is displayed after conversion to double precision.

You can enter the words "Infinity", "-Infinity" or "NaN" to get the corresponding special values for IEEE-754. Please note there are two kinds of zero: +0 and -0.

The value of a IEEE-754 number is computed as: The sign is stored in bit 32. The exponent can be computed from bits 24-31 by subtracting 127. The mantissa (also known as significand or fraction) is stored in bits 1-23. An invisible leading bit (i.e. it is not actually stored) with value 1.0 is placed in front, then bit 23 has a value of 1/2, bit 22 has value 1/4 etc. As a result, the mantissa has a value between 1.0 and 2. If the exponent reaches -127 (binary 00000000), the leading 1 is no longer used to enable gradual underflow.

Not every decimal number can be expressed exactly as a floating point number. This can be seen when entering "0.1" and examining its binary representation which is either slightly smaller or larger, depending on the last bit.