Simplify the following Boolean expressions using Boolean algebra. Show the simplification steps. a) ?(?̅? + ??̅) + ?(?? + ??̅) b) (? + ?)(?? + ??̅) + ?? + C
Part (a)
B(A'C + AC') + A(BC + BC')
= A'BC + ABC' + ABC + ABC' [By expanding]
= A'BC + ABC' + ABC [as ABC' + ABC' = ABC']
Since ABC + ABC = ABC so, we can substitute ABC by ABC + ABC
= A'BC + ABC' + ABC + ABC
= ABC' + ABC + ABC + A'BC
= AB(C + C') + BC(A + A')
= AB + BC [as C + C' = 1 and A + A' =1]
= B(A + C)
Part (b)
(A + C)(AD + AD') + AC + C
= (A + C)A(D + D') + AC + C
= (A + C)A + AC + C [as D + D' = 1]
= A + AC + AC + C
= A + AC + C [as AC + AC = AC]
= A(1 + C) + C
= A.1 + C [as 1 + C = 1]
= A + C
Hope this helps.
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