The mantissa of a floating point number???

Please see James Tursa's answer for a cautionary note about the two different definitions of mantissa! Since you asked about binary form, I expect you mean the one from the Cleve Moler article, not the Mathworld article definition (or the formula I gave).

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Joe 2013-3-17

How would I convert the mantissa to binary form?

Walter Roberson 2013-3-17

http://class.ece.iastate.edu/arun/CprE281_F05/ieee754/ie4.html

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Answer 2

James Tursa 2013-3-17

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https://ww2.mathworks.cn/matlabcentral/answers/67491-the-mantissa-of-a-floating-point-number#answer_78934

编辑：James Tursa 2013-3-17

A word or caution here. The mantissa referred to in the mathworld link above is NOT the same as the mantissa referred to in the Cleve Moler link. The Cleve Moler link refers to a number written in binary exponential notation as (1 + f) * 2^e, and the f here is the "mantissa" or fractional part (the part that is physically represented in the IEEE floating point format). This of course will not match an expression like f = x - floor(x) for an arbitrary x. A simple example would be 0.5. In the Cleve Moler link you would get f = 0, but in the mathworld link you would get f = 0.5. So which one should you use? Depends on your needs. If you are trying to dissect a specific floating point bit pattern on your machine, then typically the Cleve Moler link formula is what is usually intended. You can get at these values with the MATLAB function [F,E] = log2(X).

I would also add that the Cleve Moler link formula only applies to floating point bit patterns that use a hidden leading bit normalization scheme (like IEEE). Although most (all?) modern computers do this, it is not true in general of all computers (some actually have the leading mantissa bit present in the floating point bit pattern).