Here is an one example of how to Evaluate a Postfix expression using a stack:

Infix expression: $3+5*4$

Postfix expression: $354*+$

$3->$ push $3->(3)$

$5->$ push $5->(5,3)$

$4->$ push $4->(4,5,3)$

$*->$ evaluate operator $*->*($pop $4,$ pop $5)->5*4->20$

$20->$ push $20->(20,3)$

$+->$ evaluate operator $+->+($pop $20,$ pop $3)->3+20->23$

$23$

Given a$=2,$ b$=3,$ c $=5,$ d$=7,$ and e$=11,$ evaluate the postfix expressions of questions $($a$)-($f$)$ using a stack. Draw the intermediate stacks. Check your answer by evaluating the infix expression.

$($a$)$ a $*$ b

Prefix:

Postfix:

Evaluate Postfix using stack:

Infix:

b$)$ a $-$ b $-$ c

Prefix:

Postfix:

Evaluate Postfix using stack

Infix:

c$)($a $*$ b$)+$ c

Prefix:

Postfix:

Evaluate Postfix using stack

Infix:

d$)$ a $*$ b $-$ c $/$ d $+3$

Prefix:

Postfix:

Evaluate Postfix using stack

Infix:

e$)$ a $+4*($e $+$ d $/2)$

Prefix:

Postfix:

Evaluate Postfix using stack

Infix:

f$)$ a $$ b $($c $$ d$)$

Prefix:

Postfix:

Evaluate Postfix using stack

Infix: