Consider the set of all n$-$character strings over the alphabet: E$=$Q$,$W$,$ E$,$ R$,$ T$,$ Y$,$U$,1,0,$P$.($The first row of a standard keyboard.$)($a$)$ Using fixed length encoding, how many bits are required to encode each n$-$character string over the alphabet $\backslash$Sigma $?($b$)$ Develop a fixed length encoding for this problem. $($c$)$ Use your fixed length encoding$/$decoding for the following strings. i$.$ Encode the string: $$QUIET$$ ii$.$ Encode the string: $$TROUP$$ iii. Decode the string $($or say non$-$decodable if you cannot decode it$)$: $00000001001000110100"$ iv$.$ Decode the string $($or say non$-$decodable if you cannot decode it$)$: $10001001101010111100($d$)$ Determine the number of bits required for the theoretically optimal encoding of each n$-$character string over the alphabet $\backslash$Sigma $.($e$)$ Develop an encoding algorithm for all $5-$character strings over the alphabet that achieves the theoretically optimal number of bits. i$.$ Encode the string: "QUIET$$ ii$.$ Encode the string: "TROUP$$ iii. Decode the string $($or say non$-$decodable if you cannot decode it$)$: $"00000001001000110$ iv$.$ Decode the string $($or say non$-$decodable if you cannot decode it$)$: $"10001001101010111"$