Booth$$s algorithm to find the product of a multiplier, M$,$ and a multiplicand,

B$,$ can be summarized by the following table:

Cin Multiplier LSL # ALU Cout

$0002-$ A$+00$

$00122$N A$+$B $0$

$0102(2$N$+1)$ A$+$B $0$

$01122$N A$$B $1$

$10022$N A$+$B $0$

$1012(2$N$+1)$ A$+$B $0$

$11022$N A$$B $1$

$1112-$ A$+01$

Demonstrate how Booth$$s algorithm performs multiplication by finding the

product of $000010012($M$)$ and $010010112($B$).$ Each step in the calculation

should be given. Give the final result in a $16$ bit binary format.

$12$

b$)$ Describe the difference between a $$carry propagate$$ adder and a $$carry save$$

adder. How is a carry save adder used to improve the performance of the

multiplier circuit used in the ARM$7$ microprocessor?

$4$

c$)$ The ARM$7$ multiplier can give a double length $64$ bit product.

Why is it important to know the number format, either two$$s complement or

unsigned integer, when calculating a double length product?

$4$

d$)$ A barrel shifter is used in ARM$7$ to execute a number of instructions for

example, LSL $($logical shift left$),$ ROR $($Rotate right$)$ etc. Using appropriate

instructions, explain how a barrel shifter may be used to multiply and divide

a number by $2$n$.$

$5$

Total

$25$