deletions | additions       diff --git a/bits4.tex b/bits4.tex  index d47d421..5747ce1 100644  --- a/bits4.tex  +++ b/bits4.tex 
...
Verify that the new bit $f(x,y,z)$ is the parity bit.  \begin{Example} A check that is extremely useful is to check if a vectors of bits is the null vectors, for example $S=(x,y,z)\in \Fb^3$, where we define the "parity bit" a new bit that is $1$ if the number of bits $1$ in $S$ is odd, $0$ otherwise. To compute the parity bit we define a function $f$ on $S$, that is if the bits are $n=3$   \[  f:(\Fb)^3 \rightarrow \Fb,  \]  where $f(x,y,z)=x+y+z$.  \end{Example}  Let $f:(\Fb)^3 \rightarrow \Fb$ be a polynomial function such that