Construct the truth table for the logical function f$($a$,$b$,$c$,$d$)$ where

$(,,,)=(+)++,$

$($b$)$ Write down equivalent expressions for f in sum$-$of$-$product $($SOP$)$ form and

in canonical product$-$of$-$sums form.

$($c$)$ Demonstrate the following equivalence, where $$ is as defined in $2($a$).$

$(,,,)=[(+,+)(++)(+,+)]$

$3.$ Karnaugh Maps

Simplify the following logical formulae using Karnaugh maps $($or otherwise$)$:

$($a$)!=$

a$($

b$+)+$

b$+,$

$($b$)"=,+,,++,$

$($c$)$# $=()()++3+3$

$($d$)$$ $=4$

$1$ if $.$ or $.<$

$0$ if $,.$ or $<..<$

don$$t care otherwise

G

$($e$)$ What are the most complex Karnaugh maps with four variables, i$.$e$.$ the

ones that give the sum$-$of$-$product formulae with most terms?