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How to determine the set of real numbers corresponding to a given floating point number?

Short answer: If the mantissa is not all ones, the next floating-point number is $1$ ulp more. E.g. $1.1000_b\times 2^7\to1.1001_b\times 2^7$ ($192_d\to200_d$), the difference is $2^{7-4}=8$. If the ...
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Floating-point rounding - bit patterns of values that are halfway between two possible results

Let us express any given binary number without a floating point in the following form $$\underbrace{XX\cdots X}_{i\text{ digits}}~Y~\underbrace{ZZ\cdots Z}_{j\text{ digits}}{}_2=x\times2^{j+1} + Y\...
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