this is for holding javascript data
Michela Ceria edited bits4.tex
about 6 years ago
Commit id: 955c84dbfe4a3a25eff8021a8511155904e64582
deletions | additions
diff --git a/bits4.tex b/bits4.tex
index 250820b..af9ca2b 100644
--- a/bits4.tex
+++ b/bits4.tex
...
Verify that the function $p(x,y,z)$ returns the parity bit.
\end{Exercise}
\begin{Example} \label{Prodotto1} \begin{Example}\label{Prodotto1}
We are interested in a function that returns $1$ if a vector of bits is null, $0$ otherwise.
This is a useful Boolean function, since it recognizes if a vector of bits is the null vector $(0,\ldots,0)$. \\
We now show how to obtain a polynomial representing this function. We observed in Exercise \ref{XorIsNice} that the multiplication of bits has the same truth table of the $\AND$ operator. In particular we have $1$ if each bit is $1$, $0$ otherwise. This is the opposite of what we want and so we can add $1$ to have the sought-after function (see Exercise \ref{Not}). For example, if $n=3$ the function in $\Fb[x,y,z]$ is $$(x,y,z) \mapsto xyz+1.$$