IEEE Converter

IEEE Floating Point Converter

This tool converts a double-precision floating-point number to its IEEE representation.

Decimal number:

IEEE bits:

Information

Notes on converting from floating-point format to IEEE:

For an input x, the converter provides the bits for fl(x), the floating-point number closest to x.

Only rational numbers of the form m/2^n can be represented exactly. For example, 11/8 = 1.375 can be represented exactly but 0.1 cannot.
The greatest consecutive integer that can be represented exactly (i.e. flintmax) is 2^53 = 9007199254740992. Integers above this magnitude, such as 10^30, are not guaranteed to be represented exactly.

Scientific notation such as -1.1e2 is supported. Expressions such as 2^5, 2+2, and 11/8 are not.
Any ill-formatted input will evaluate to NaN.

Notes on converting from IEEE to floating-point format:

Any whitespace in the input binary string is ignored.
If the input is less than 64 bits, zeros will be appended to the end automatically.
If the input is greater than 64 bits, any extra bits at the end will be chopped.
The converter prints a warning if the input is not exactly 64 bits. However, if you do include whitespaces, it does not check that the inputs have respective lengths 1, 11, and 52.