Problem $2($ Effect of Variable Ordering in BDD construction$).$ In this problem we will revise

how variable ordering can affect the BDD construction. Consider the following Boolean function:

f $=($ a$.$b $+$ c $)$ cd $$

$1.$ Construct the ROBDD for this function using recursive Shannon decomposition and reduc$-$

tion for the given variable ordering. What is the effect of the variable ordering? $[$ Points :

$10]$

$($a$)$ a $<$ b $<$ c $<$ d

$($b$)$ c $<$ a $<$ b $<$ d