Web Reference: Yes, this is correct. For one thing, there are numbers that cannot be represented with a finite length. One of the most notable is $1/10$. In a binary representation, this is the repeating, non-terminating decimal $0.0\overline {0011}$. Also, for a given precision (Let's say $24$, since that is that precision of 32-bit IEEE-$754$ floating point numbers, like the float type of Java or C), there ... The format and arithmetic of floating point numbers is described by several standards. For instance, IEEE 754 is a widely used standard for the case b=2. It considers, amongst other things, single-precision numbers: - 32 bits: 1 bit sign, 8 bits exponent, 23 bits mantissa, bias 127 - range: approx. ± 3.403 × 10^38 Nov 25, 2018 · You cannot expect to use integer binary addition on two floating-point representations and get a meaningful result. First, $1.111$ cannot be represented exactly in binary floating point.
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