As per the given question,
Total number of available key(n) =108
Probability to press any one key P(x)=1081
As per the Shanon entropy theorem,
=−ΣnP(x)log(P(x)1)
=−Σn108log(1/1081)
=−108×1081log(108)
=−log(108)
Similarly, For touch pad,
Total number of key (n)=16
Probability of press any one key P(x)=161
=−ΣnP(x)log(1/P(x)1)
=−16×161log(1/16)1
=−log(16)
Hence, from the above it is clear that this information is more than the information carried by a key on the number pad of a touch tone telephone.
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