a$.$ If you are working in a k$-$ary system $($for example, binary has $2($k$=2)$ distinct symbols, $0$ and $1$; decimal has $10($k$=10)$ distinct symbols $0,1,2,3,...9),$ and you have a sequence of n characters $($a character may take one of k different symbols$),$ then how many numbers can you represent with this sequence?b$.$ Given a set of m numbers, what is the minimum length of the sequence of characters required to represent each member of this set uniquely in a k$-$ary system?c$.$ How does this scale with k$?$ An increase in k will decrease or increase the minimum length of the sequence? d$.$ If you answered decrease, then clearly, a larger k can represent more numbers with a shorter sequence. Then why do we use k $=2$ in most computer systems? Why not a higher k$?$