Problem $1[24$ pts: $(6$ each$)]$: Base conversions

i Convert the number $947$ from decimal to binary using Euclid$$s Division Algorithm.

ii Convert the binary number $(11010011)2$ to decimal. Show an intermediate step which shows

each powers of two to be added.

iii Convert the decimal number $174$ to base $16($hexadecimal$)$ using Euclid$$s Division Algorithm.

iv Solve for the decimal value x:

$(2$F $3)16=($x$)10$

Problem $2[23$ pts: $(14,9)]2$s Complement & Overflow

i Give the $8-$bit two$$s complement representations of the following decimal values: $73,97,65,$

$94.$ Give some justification with responses for any negative values.

ii Compute the following operations as a computer would, directly from the $(8-$bit$)2$s complement

representations above. Indicate whether each operation results in an overflow or not.

Note: Use the two$$s complement representations from part ii above.

$($a$)65+73$

$($b$)6594$

$($c$)97+73$

Problem $3[16$ pts: $(8$ each$)]$: Expressiveness of a number representation

$1.$ What range of numbers can be represented in $6-$bit two$$s complement?

$2.$ What are the minimum number of bits necessary to represent $1234$ in two$$s complement?