How many bits are needed for presentation of a $3-$digit unsigned decimal number in the binary

form?

$2.$ Convert decimal number $168$ to the hex form using division by $16.$ Convert the hex form of the

number to the binary form.

$3.$ An unsigned fractional decimal number has to be converted to the $10-$bit binary form. Estimate

the maximum conversion error for this case. Present the answer in the decimal form with a $2-$digit

mantissa $($MM$)$ and an exponent $($EE$)$: MM x $10^$EE

$4.$ a$)$ Convert decimal fraction $0\mathrm{.}3$ into the $10-$bit unsigned form by repeated multiplication by $2$

saving the integer parts. Identify the repeated pattern.

b$)$ Obtain the $20-$bit unsigned form for decimal number $0\mathrm{.}6$ by using the answer in part b:

multiply by $2$ the answer in question $4$a by shifting the binary point, duplicate the repeated

pattern.

$5.$ Show the most positive and the most negative $8-$bit signed integers and their decimal equivalents.

Negative numbers are presented as $2$s complements.

$6.$ Binary numbers A $=11001110$ and B $=00011110$ are presented in the $8-$bit signed integer format

described in question $5$ above.

a$)$ Show the $1$s complements and the $2$s complements of A and B$.$

b$)$ Perform the bit$-$by$-$bit addition of A and B$,$ show carries. Determine both sign and decimal

magnitude of the sum.

c$)$ Obtain A $$ B by bit$-$by$-$bit addition of A and $(-$B$).$ Use the $2$s complement of B$,$ show carries.

Identify the sign of the result. Determine the decimal magnitude of the result.

d$)$ Obtain B $-$ A by bit$-$by$-$bit addition of B and $(-$A$).$ Use the $2$s complement of A$,$ show carries.

Identify the sign of the result and determine the decimal magnitude of the result.