Problem #$1$

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

$1.$ Radix$-2$ conventional system.

$2.$ Radix$-8$ conventional system.

$3.$ Radix$-17$ conventional system.

$4.$ Mixed radix with radix vector R $=($n$+1,$ n$,...,3,2)$ 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 digitvector.