$1.$ Show the step$-$by$-$step multiplication process using Booth algorithm when the following binary numbers are multiplied. Assume $5-$bit registers that hold signed numbers. The multiplicand is $$

$$

a$.(-17)$ x $(-14)$

b$.(-16)$ x $(+14)$

$$

$2.$ Show the content of registers A$,$ B$,$ Q$,$ and SC during the decimal multiplication of

$$

$($a$)470$ x $152$ and

$($b$)999$ x $199.$

$$

Assume three$-$digit registers and take the second number as the multiplier.

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$3.$ Show the content of registers A$,$ E$,$ Q$,$ and SC during the decimal division of $1680/32.$ Assume two$-$digit registers.

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$4.$ Show the contents of registers E$,$ A$,$ Q$,$ and SC during the process of multiplication of two binary numbers, $11111($multiplicand$)$ and $10101($multiplier$).$ The signs are not included.

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$5.$ Show the contents of registers E$,$ A$,$ Q$,$ and SC during the process of division of

$($a$)10100011$ by $1011$;

$($b$)00001111$ by $0011.($Use a dividend of eight bits.$)$

$$

$6.$ When the following signed$-$magnitude numbers are computed. In each case give the value of AVF. The leftmost bit in the following numbers represents the sign bit.

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a$.0101101+0011111$

b$.1011111+1101101$

c$.0101101-0011111$

d$.0101101-0101101$

e$.1011111-0101101$

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$7.$ Perform the arithmetic operations below with binary numbers and with negative numbers in signed$-2$s complement representation. Use seven bits to

accommodate each number together with its sign. In each case, determine if there is an overflow by checking the carries into and out of the sign bit position.

$$

a$.(+35)+(+40)$

b$.(-35)+(-40)$

c$.(-35)-(+40)$