Practice for computer arithmetic

For all questions, please show your computation clearly.

Consider Fig. B$\mathrm{.}5\mathrm{.}12($from book$/$lecture note$)$ and explain clearly how slt instruction is

manipulated in the $32-$bit ALU.

Also, explain why control signal values for slt instruction are $\text{'}0111\text{'}.$

Consider the unsigned number multiplication hardware that we discussed in class.

Assume that the hardware is used for unsigned $4-$bit number multiplication $(0101**1110{)}_{?}.$

Show the contents of registers for each step of the multiplication using the $2-$step multiplication

algorithm.

Consider the Booth's algorithm for $2\text{'}$s complement number multiplication.

$($a$)$ Show Booth's recoded number for binary value $(1010011101)$ and justify your answer.

$($b$)$ For $({1010}_{*}*0101),$ i$.$e$.,(-6)**5$ in decimal, show the contents of registers for each step.

Perform the restoring division for $(\frac{1011}{0100}),$ i$.$e$.,\frac{11}{4}$ in decimal, and show the contents

of registers for each step. Also show the resulting quotient and remainder in binary numbers.

Perform the non$-$restoring division for $(\frac{1011}{0100}),$ i$.$e$.,\frac{11}{4}$ in decimal, and show the contents

of registers for each step. Also show the resulting quotient and remainder in binary numbers.

Explain briefly how the non$-$restoring division algorithm achieves higher efficiency

than the restoring division algorithm.