deletions | additions       diff --git a/bits4.tex b/bits4.tex  index ae750c8..a5a54dd 100644  --- a/bits4.tex  +++ b/bits4.tex 
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Verify that the function $p(x,y,z)$ returns the parity bit.  \end{Exercise}  \begin{Example} An We are interested in a function that returns $1$ if a vector of bits is null, $0$ otherwise.  This is  extremely useful boolean Boolean  function, is the one that recognize since it recognizes  if a vector of bits is the nullvectors, that is $(0,\ldots,0)$. This function returns $1$ if the  vector is null, $0$ otherwise. $(0,\ldots,0)$.  We observed (see \ref{XorIsNice}) that the multiplications of bits has the same truth table of the $\AND$ operator. So we have $1$ if each bit is $1$, $0$ otherwise. That is the opposite that we want. Adding $1$ we have the function (see \ref{Not}). If $n=3$ we have where $z(x,y,z)=xyz+1$. \end{Example}  \begin{Example} In \ref{XorIsNice} we observed that the operator $\OR$ is neither the summand in $\Fb$ (that is $\XOR$) nor the multiplication in $\Fb$ ($\AND$). We would like to define a boolean Boolean  function $o(x,y)$ that corresponds to the $\OR$ operator. We recall the famous De Morgan law: \[  \NOT(x\, \OR \, y)=\NOT(x)\, \AND\, \NOT(y)  \] 
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\end{Example}  \begin{Exercise}  Find the boolean Boolean  function $o(x,y,z)$ that corresponds to $x\, \OR\, y\,\OR \,z$. \end{Exercise}