  We study the effects of finite-precision representation of source's
probabilities on the efficiency of classic source coding algorithms, such as
Shannon, Gilbert-Moore, or arithmetic codes. In particular, we establish the
following simple connection between the redundancy $R$ and the number of bits
$W$ necessary for representation of source's probabilities in computer's memory
($R$ is assumed to be small): \begin{equation*} W \lesssim \eta \log_2
\frac{m}{R}, \end{equation*} where $m$ is the cardinality of the source's
alphabet, and $\eta \leqslant 1$ is an implementation-specific constant. In
case of binary alphabets ($m=2$) we show that there exist codes for which $\eta
= 1/2$, and in $m$-ary case ($m > 2$) we show that there exist codes for which
$\eta = m/(m+1)$. In general case, however (which includes designs relying on
progressive updates of frequency counters), we show that $\eta = 1$. Usefulness
of these results for practical designs of source coding algorithms is also
discussed.
