Assume that the top of the stack in a program is pointed to by the register SP$.$ You are required to write program segments to perform each of the following tasks $($assume tha the following addressing modes are available: indexed, autoincrement, and autodecrement$).$

$($a$)$ Pop the top three elements of the stack, add them, and push the result

back onto the stack.

$($b$)$ Pop the top two elements of the stack, subtract them, and push the results

back onto the stack.

$($c$)$ Push five elements $($one at a time$)$ onto the stack.

$($d$)$ explain the circumstances under which indirect addressing is really needed.