Compare $0-,1-,2-,3-$ and $4-$address machines by writing programs to compute

the Taylor series expansion of sine$($x$)$:

SIN X $=$ X $1/3!$ X$3+1/5!$ X$5$

The instructions available for use are as follows:

$0-$address $1-$address $2-$address $3-$address

PUSH M LOAD M MOV X$,$ Y MOV X$,$ Y

POP M STORE M ADD X$,$ Y ADD X$,$ Y$,$ Z

ADD ADD M SUB X$,$ Y SUB X$,$ Y$,$ Z

SUB SUB M MUL X$,$ Y MUL X$,$ Y$,$ Z

MUL MUL M DIV X$,$ Y DIV X$,$ Y$,$ Z

DIV DIV M

DUP

Assume that you can replace any operand with a constant value in all machines, e$.$g$.$

PUSH $3,$ puts the constant $3$ onto the stack. You must calculate the factorial values.

In these instructions, opcodes are $8$ bits long; M is a $16-$bit memory address; X$,$ Y$,$

and Z are $16-$bit addresses $($or $8-$bit constants$).$ The data $($operand$)$ size is $32$ bits.

The zero$-$address machine uses a stack and the $1-$address machine uses an

accumulator. The DUP instruction duplicates the top of the stack, so the same value

appears twice.

The variables are initially stored in main memory, and the result $($sin$($x$))$ must be

stored back to memory into memory location SIN. Code the program for each

machine as compactly as possible, and calculate how many bits of memory traffic

are used to compute sin$($x$)$ ONLY for $3-$address machine.