Question

A computer key board has 108 keys. Assuming equal probability of any key pressing calculate the information content, I, carried by each key. Prove that this information is more than the information carried by a key on the number pad of a touch tone telephone. [Hint: Touch phone has 16 keys on its pad]

Answer 1

The associated information gain for the keyboard with every key having probability of 1/108 is

$$I_k=-\text{log}_2\frac{1}{108}=6.75.$$

For the phone this information is

$$I_p=-\text{log}_2\frac{1}{16}=4.$$