Computer Arithmetic

$($a$)$ Determine how many digits are necessary to represent integers in the range $0$ to $(297{)}_{10}$ using

Radix$-2$ conventional system.

Radix$-8$ conventional system.

Radix$-17$ conventional system.

Mixed radix with radix vector $R=(n+1,n,$dots,$3,2)$ and canonical digit$-$set.

$($b$)$ What is the largest integer that can be represented by the digit$-$vectors of the size determined in

each of the cases in part$-$a$?$

$($c$)$ Specify a coding for the digits and determine the number of bits of the bit$-$vector that represents

these integers in part$-$a$.$ Determine the efficiency of each representation, defined as the ratio of

the number of bits in the binary representation and number of the bits required by the digit$-$

vector.