X-Git-Url: https://git.ucc.asn.au/?p=ipdf%2Fsam.git;a=blobdiff_plain;f=chapters%2FBackground%2FFixedPoint.tex;h=352e9d303fae6b899d9e680b287e07867ee6f64f;hp=707dab23c218acde789c5fb1e92e2c03d16e7d79;hb=689e433b348588e05f47d23385dbf05d239c95d2;hpb=9fcf44a0c34f393689118e913a2d17d907036c85 diff --git a/chapters/Background/FixedPoint.tex b/chapters/Background/FixedPoint.tex index 707dab2..352e9d3 100644 --- a/chapters/Background/FixedPoint.tex +++ b/chapters/Background/FixedPoint.tex @@ -3,7 +3,7 @@ A positive real number $z$ may be written as the sum of smaller integers digit z &= \displaystyle\sum_{i=-\infty}^{\infty} d_i \beta^{i}\label{fixedpointZ} \end{align} Where each digit $d_i < \beta$ the base. A set of $\beta$ unique symbols are used to represent values of $d_i$. -A seperate sign '-' can be used to represent negative integers using equation \eqref{fixedpointZ}. +A seperate sign '-' can be used to represent negative reals using equation \eqref{fixedpointZ}. To express a real number using equation \eqref{fixedpointZ} in practice we are limited to a finite number of terms between $i = -m$ and $i = n$. Fixed point representations are capable of representing a discrete set of numbers $0 \leq |z| \leq \beta^{n+1}-\beta^{-m}$ seperated by $\Delta z = \beta^{-m} \leq 1$. In the case $m = 0$, only integers can be represented. @@ -13,7 +13,7 @@ Example integer representation in base 10 (decimal) and base 2 (binary): 1011000110010_2 &= 1\times2^{12} + 0\times2^{11} + \text{ ...} + 0\times2^0 \end{align*} - +{\bf FIXME} Add Maths reference (Cantor's Diagonal argument) without going into all the Pure maths details