+The use of floating point arithmetic in computer systems was pioneered by Knuth, Goldberg\cite{goldbern1967twentyseven}, Dekker, and others\cite{HFP}, but modern systems are largely compatable with the IEEE-754 standard pioneered by William Kahan in 1985 \cite{ieee754std1985} and revised (also with contributions from Kahan) in 2008\cite{ieee754std2008}. Recently, the ``Handbook of Floating Point Arithmetic''\cite{HFP} by Muller et al (2010) provides a detailed overview of IEEE-754 floating point arithmetic.
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Whilst a Fixed Point representation keeps the ``point'' (the location considered to be $i = 0$ in \eqref{fixedpointZ}) at the same position in a string of bits, Floating point representations can be thought of as scientific notation; an ``exponent'' and fixed point value are encoded, with multiplication by the exponent moving the position of the point.
-The use of floating point arithmetic in computer systems was pioneered by Knuth, Goldberg{goldbern1967twentyseven}, Dekker, and others\cite{HFP}, but modern systems are largely compatable with the IEEE-754 standard pioneered by William Kahan in 1985 \cite{ieee754std1985} and revised (also with contributions from Kahan) in 2008\cite{ieee754std2008}.
A floating point number $x$ is commonly represented by a tuple of values $(s, e, m)$ in base $B$ as\cite{HFP, ieee2008-754}: $x = (-1)^{s} \times m \times B^{e}$
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