Simplifythe following expressions using the laws and theorems of Booleanalgebra:
ID: 3616131 • Letter: S
Question
Simplifythe following expressions using the laws and theorems of Booleanalgebra: Y(A,B,C,D) = A'B'C'D' + A'B'C'D + A'B'CD' +A'B'CD + AB'C'D' + AB'CD' so that it will equal to B'D' +A'B' Please specifly which theorems or laws you usedto simplify. Thank you Simplifythe following expressions using the laws and theorems of Booleanalgebra: Y(A,B,C,D) = A'B'C'D' + A'B'C'D + A'B'CD' +A'B'CD + AB'C'D' + AB'CD' so that it will equal to B'D' +A'B' Please specifly which theorems or laws you usedto simplify. Thank youExplanation / Answer
A'B'C'D' + A'B'C'D + A'B'CD' + A'B'CD + AB'C'D' + AB'CD'
= A’B’C’(D’+D) +A’B’C(D’+D) + AB’D’(C’+C)
= A’B’C’(1) + A’B’C(1) +AB’D’(1) (From Laws of complementarity: X + X' = 1)
= A’B’C’ + A’B’C +AB’D’
= A’B’(C’+C) +AB’D’
= A’B’(1) + AB’D’(From Laws of complementarity:X +X' = 1)
= A’B’ + AB’D’
= B’(A’+AD’)
= B’(A’+A)(A’+D’) (From distributivelaw: X + YZ = ( X + Y ) ( X + Z )
= B’(1)(A’+D’) (From Laws ofcomplementarity: X + X' = 1)
= B’(A’+D’)
= B’(D’+A’)
= B’D’+A’B’