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Spell IEEE-754 consistently.

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John Winans 2020-08-18 18:56:52 -05:00
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book/float/chapter.tex
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@ -107,11 +107,11 @@ normalized values by adding 1 to the significand.
%\item $-((1 + \frac{1}{4} + \frac{1}{16}) \times 2^{128-127}) = -(1 \frac{5}{16} \times 2^{1}) = -(1.3125 \times 2^{1}) = -2.625$ %\item $-((1 + \frac{1}{4} + \frac{1}{16}) \times 2^{128-127}) = -(1 \frac{5}{16} \times 2^{1}) = -(1.3125 \times 2^{1}) = -2.625$
\item $-((1 + \frac{1}{4} + \frac{1}{16}) \times 2^{128-127}) = -((1 + \frac{1}{4} + \frac{1}{16}) \times 2^1) = -(2 + \frac{1}{2} + \frac{1}{8}) = -(2 + .5 + .125) = -2.625$ \item $-((1 + \frac{1}{4} + \frac{1}{16}) \times 2^{128-127}) = -((1 + \frac{1}{4} + \frac{1}{16}) \times 2^1) = -(2 + \frac{1}{2} + \frac{1}{8}) = -(2 + .5 + .125) = -2.625$
\item IEEE754 formats: \item IEEE-754 formats:
\begin{tabular}{|l|l|l|} \begin{tabular}{|l|l|l|}
\hline \hline
& IEEE754 32-bit & IEEE754 64-bit \\ & IEEE-754 32-bit & IEEE-754 64-bit \\
\hline \hline
sign & 1 bit & 1 bit \\ sign & 1 bit & 1 bit \\
exponent & 8 bits (excess-127) & 11 bits (excess-1023) \\ exponent & 8 bits (excess-127) & 11 bits (excess-1023) \\
@ -127,7 +127,7 @@ the sign is zero, the number represents positive infinity.
\item When the exponent is all ones, the mantissa is all zeros, and \item When the exponent is all ones, the mantissa is all zeros, and
the sign is one, the number represents negative infinity. the sign is one, the number represents negative infinity.
\item Note that the binary representation of an IEEE754 number in memory \item Note that the binary representation of an IEEE-754 number in memory
can be compared for magnitude with another one using the same logic as for can be compared for magnitude with another one using the same logic as for
comparing two's complement signed integers because the magnitude of an comparing two's complement signed integers because the magnitude of an
IEEE number grows upward and downward in the same fashion as signed integers. IEEE number grows upward and downward in the same fashion as signed integers.