Answer to Question #37124 in Electromagnetism for Anurodh

Question #37124

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 the keys on the key pad of a touch tone telephone. [ Hint. Touch phone has 16 keys on its pad].

information, I = k ln (n_before / n_after), where k = 1/ln(2) to give answer in bits. n_before:= total number of possible states before message is received (108 possible states per key) n_after:= total number of possible states after message received ( in this case 1, since once you press a key you get 1 response) So I per key = ln(n_before / n_after ) = 1/ln(2) (108 / 1) = 6.8bits / key if n_before is 16 = 1/ln(2) (16/1) = 4 bits / key

## Comments

Valentin Uzunov16.04.16, 22:30information, I = k ln (n_before / n_after), where k = 1/ln(2) to give answer in bits.

n_before:= total number of possible states before message is received (108 possible states per key)

n_after:= total number of possible states after message received ( in this case 1, since once you press a key you get 1 response)

So I per key = ln(n_before / n_after )

= 1/ln(2) (108 / 1) = 6.8bits / key

if n_before is 16

= 1/ln(2) (16/1) = 4 bits / key

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