X-Git-Url: https://git.ucc.asn.au/?p=ipdf%2Fsam.git;a=blobdiff_plain;f=chapters%2FBackground%2FFixedPoint.tex;h=bb1dea355f69d542fe516e868196c11928071b83;hp=4ef2f6ca7e75b7f613cc31859b59102723a5c3eb;hb=7fe12ce195f039925222ad98b38018ad31d1b1f2;hpb=ae8d5f837db032eb4d9e9666f5026fab7e3e8e4a diff --git a/chapters/Background/FixedPoint.tex b/chapters/Background/FixedPoint.tex index 4ef2f6c..bb1dea3 100644 --- a/chapters/Background/FixedPoint.tex +++ b/chapters/Background/FixedPoint.tex @@ -1,6 +1,6 @@ A positive real number $z$ may be written as the sum of smaller integers ``digits'' $d_i$ multiplied by powers of a base $\beta$. \begin{align} - z &= d_0 \beta^0 + d_1 \beta^1 + d_2 \beta^2 + \text{ ...} = \displaystyle\sum_{i=-\infty}^{\infty} d_i \beta^{i}\label{fixedpointZ} + z &= \text{... } + d_{-1} \beta^{-1} + d_0 \beta^0 + d_1 \beta^1 + \text{ ...} = \displaystyle\sum_{i=-\infty}^{\infty} d_i \beta^{i}\label{fixedpointZ} \end{align} Where each digit $d_i < \beta$. A set of $\beta$ unique symbols are used to represent values of $d_i$. A seperate sign '-' can be used to represent negative reals using equation \eqref{fixedpointZ}.