Assume numbers are represented in $8-$bit twos$-$complement representation. Show the calculation of the

following:

A$.{33}_{10}-{14}_{10}$

B$.{24}_{10}-{43}_{10}$

C$.-{44}_{10}-{13}_{10}$

Use the Booth algorithm to multiply the following numbers $[$ M: Multiplicand and Q: Multiplier$]$

A$.M=14$ and $Q=-10($number is represented using $6$ bits$)$

B$.M=63$ and $Q=-17($number is represented using $8$ bits$)$

Use the Restoring algorithm for division. $[$ M: Divisor and Q: Dividend$]$

A$.M=7$ and $Q=19($use a $6-$bit register$)$

B$.M=13$ and $Q=96($use an $8-$bit register$)$

Using a floating number arrangement, A computer stores a number in $32$ bits. Express the following numbers

in IEEE $32-$bit floating point format.

A$.27\mathrm{.}75$

B$.-37\mathrm{.}875$

A computer stores the floating number in $32$ bits, where $1$ bit is for the sign, $8$ bits are for the exponent

having a bias or $(+127),$ and mantissa has $23$ bits. What is the decimal value of the given numbers:

A$.$ If the computer represents a number as $(11000001011110110000000000000000$