Problem $1.$ To represent $26$ characters in English $($ignore cases$)$ using a binary language, we need $5$ digits $($bits$),$ because $25=32,$ which is greater than $26.$ Suppose one language has $48$ characters. Using binary language $($each bit has values $0$ or $1)$ of modern computers, how many digits $($bits$)$ would be needed to represent the entire character set? Assuming that a different electronic computer uses a ternary language $($each bit has three values $0,1,$ or $2),$ how many digits $($bits$)$ in the ternary language would be needed to represent the $48$ characters?

Problem $2.$ Convert decimal $($base $10)$ number $2021$ to $(1)$ binary representation; $(2)$ octal representation; and $(3)$ hexadecimal representation. Show your work step by step.

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