write the canonical product and canonical sum of the followinglogic function. F(
ID: 1831079 • Letter: W
Question
write the canonical product and canonical sum of the followinglogicfunction.
F(A, B, C, D) = A•B + C•D + A•D
use switching algebra theorems to simplify each of the followinglogic
functions. list the theorems you use in each step
b) F = A•B + A•B•D•E +A•B•C•E +A•B•C•E +A•B• (C+E)
c) F = M•R•P +Q•O•R+M•N+O•N•M +Q•P•M•O +N•M•Q•R
if you can't answer all of these by the cutoff time, i'd reallyjust need the first one listed since i just want to check if i didthe last two correctly, thanks! (i'd still like an answer to thefirst after cutoff time)
Explanation / Answer
F = A'B + C'D + AD To express into canonical product form, multiply each term byX+X' where X is the missing variable in the term F = A'B(C+C')(D+D') + (A+A')(B+B')C'D + A(B+B')(C+C')D Expanding F = A'BCD + A'BCD' + A'BC'D+A'BC'D' + ABC'D + AB'C'D + A'BC'D+ A'B'C'D + ABCD+AB'CD + ABC'D+AB'C'D F = A'BCD + A'BCD' + A'BC'D+A'BC'D' + ABC'D+ AB'C'D + A'B'C'D + ABCD + AB'CD+ABC'D F = A'B + C'D + AD F =(A'+C'+A)(A'+D+A)(A'+C'+D)(A'+D+D)(B+C'+A)(B+D+A)(B+C'+D)(B+D+D) b) F = AB + ABDE +ABCE +ABCE + AB (C+E) F = AB(1+DE') + A'C'E(B+B') +A'B(C+E') Takingout the common terms F = AB +A'C'E + +A'BC +A'BE' Applying the rule 1+X=1 and X+X' = 1 F = B(A+A'C) + A'C'E + A'BE' F = B(A+C) + A'C'E +A'BE' Applyingrule X+X'Y = X+Y F = BA + BC +A'C'E + A'BE' F = B(A+A'E') + BC + A'C'E F = B(A+E') + BC + A'C'E F = AB + BE' + BC +A'C'E F = B(A+E'+C) + A'C'E F = B(A'C'E)' + A'C'E F = BP' + P WherP = A'C'E F = B + P F = B + A'C'E F = B(A+E'+C) + A'C'E F = B(A'C'E)' + A'C'E F = BP' + P WherP = A'C'E F = B + P F = B + A'C'E c) F = MRP + QOR+MN+ONM + QPMO + NMQR F = MRP +QOR+MN(1+O+QR') + QPMO' F = MRP +QOR+MN + QPMO'Related Questions
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