$1$ Perform the following base conversions using subtraction or div$-$

remainder

a$)45810=\_\_\_\_\_\_\_\_3$

c$)440110=\_\_\_\_\_\_\_9$

e$)23025=\_\_\_\_\_\_\_10$

$2.$ Convert the following decimal fractions to binary with a maximum of six

places to the right of the binary point:

a$)25\mathrm{.}84375$

d$)27\mathrm{.}59375$

e$)105\mathrm{.}59375$

$3.$ Convert the following binary fractions to decimal:

a$)10111\mathrm{.}1101$

b$)100011\mathrm{.}10011$

d$)11000010\mathrm{.}111$

$4$a$.$ Convert $36\mathrm{.}1238$ to base $10$

b$.$ Convert $370\mathrm{.}355$ base $8$ to base $10$

c Convert $7$A$0116$ to binary number.

d$.$ Convert the hexadecimal number BEEF to base $4.$

$5.$ Represent the following decimal numbers in binary using $8-$bit signed

magnitude, one's complement, two's complement, and excess$-127$

representation: $[$Please enter NA where there is no answer to the question.

$6.$ Represent the following decimal numbers in binary using $8-$bit signed

magnitude,

Value One$$s Compliment Two$$s Compliment Excess

$128$

$77\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$-42\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$119\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$-107\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$7.$ Represent the following decimal numbers in binary using $8-$bit signed

magnitude, one$$s complement, and two$$s complement representations:

Value Signed Magnitude One$$s Compliment Two$$s

Compliment

$-60\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$80\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$-20\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$8.$ Represent the following decimal numbers in binary using $8-$bit format,

Sign Magnitude One$$s Compliment Two$$s Compliment

Excess $-127$

$97\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$44\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$-44\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$9.$ Represent $\mathrm{.}4154\backslash$times $104$ in a normalized base $8$ floating point format with a sign bit, followed by a $3-$bit

excess $4$ exponent, followed by four base $8$ digits