# Questions tagged [floating-point]

Approximate representation of numbers as a fixed number of digits multiplied by a logarithmic scale.

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### Why floating point representation uses a sign bit instead of 2's complement to indicate negative numbers

Consider a fixed point representation which can be regarded as a degenerate case of a floating number. It is entirely possible to use 2's complement for negative numbers. But why is a sign bit ...
146 views

### Difference between ways to compare floating-point numbers

There seems to be many approaches to judge whether two floating-point numbers are identical. Here are some examples I've found: ...
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### Proof that a guard digit bound the error of subtraction

I was reading What Every Computer Scientist Should Know About Floating-Point Arithmetic, which is extremely interesting. But I have some troubles understanding the proof of Theorem 9 (page 33). First ...
595 views

### Convert a decimal floating-point number into a binary floating-point number

Let's say I have a decimal floating-point number, i.e. a mantissa and precision (negative exponent), both represented as integers. How do I convert this into a binary floating point number (of the ...