Given a 5-symbol alphabet with static probabilities of .1, .1, .15, .25, .4
for symbols a-e, respectively, show the steps a decimal arithmetic encoder would follow
when encoding the message acede, and give the shortest decimal arithmetic code
for this message (caution!). Compare this with the theoretically achieveable length of
this message in decimal digits. Show your work carefully, including the lower
and upper bounds after each encoding step.
Finally, decode your message, again showing the steps clearly.