Apr 28, 2022 #1 S sxy Newbie Joined Apr 28, 2022 Messages 5 Helped 0 Reputation 0 Reaction score 0 Trophy points 1 Activity points 34 Hi Why the folllowing equation is correct: L'C+I'C+L'I=L'C+L'I thanks
Apr 28, 2022 #2 andre_luis Super Moderator Staff member Joined Nov 7, 2006 Messages 9,595 Helped 1,190 Reputation 2,399 Reaction score 1,208 Trophy points 1,403 Location Brazil Activity points 55,686 Did you try put these terms into the K-map ? There you can find out what terms can be simplified. Upvote 0 Downvote
Apr 28, 2022 #3 S std_match Advanced Member level 4 Joined Jul 9, 2010 Messages 1,304 Helped 463 Reputation 926 Reaction score 448 Trophy points 1,363 Location Sweden Activity points 10,180 sxy said: Hi Why the folllowing equation is correct: L'C+I'C+L'I=L'C+L'I thanks Click to expand... It is obviously not correct. The right side always depends on L. The left side can be true regardless of L. Upvote 0 Downvote
sxy said: Hi Why the folllowing equation is correct: L'C+I'C+L'I=L'C+L'I thanks Click to expand... It is obviously not correct. The right side always depends on L. The left side can be true regardless of L.
Apr 29, 2022 #4 K kaz1 Full Member level 6 Joined Aug 15, 2019 Messages 322 Helped 18 Reputation 35 Reaction score 51 Trophy points 28 Location UK Activity points 1,921 sxy said: Hi Why the folllowing equation is correct: L'C+I'C+L'I=L'C+L'I thanks Click to expand... Using consensus theorem (XY + X'Z + YZ = XY + X'Z) let L' = X let C = Y let I = Z Hence your expression becomes: XY + Z'Y + XZ rearrange as XZ + YZ' + XY Hence based on above theory XY is redundant: = XZ + YZ' i.e. = I'C + L'I So either I or you may have typing error. Upvote 0 Downvote
sxy said: Hi Why the folllowing equation is correct: L'C+I'C+L'I=L'C+L'I thanks Click to expand... Using consensus theorem (XY + X'Z + YZ = XY + X'Z) let L' = X let C = Y let I = Z Hence your expression becomes: XY + Z'Y + XZ rearrange as XZ + YZ' + XY Hence based on above theory XY is redundant: = XZ + YZ' i.e. = I'C + L'I So either I or you may have typing error.
May 1, 2022 #5 S sxy Newbie Joined Apr 28, 2022 Messages 5 Helped 0 Reputation 0 Reaction score 0 Trophy points 1 Activity points 34 kaz1 said: Using consensus theorem (XY + X'Z + YZ = XY + X'Z) let L' = X let C = Y let I = Z Hence your expression becomes: XY + Z'Y + XZ rearrange as XZ + YZ' + XY Hence based on above theory XY is redundant: = XZ + YZ' i.e. = I'C + L'I So either I or you may have typing error. Click to expand... Hi If you do the truth table for every side of the equation; you will see that they are equal to each other; but I didn't succed to prove in in the terms of Boolean Algebra. thank you very much for your answer. Upvote 0 Downvote
kaz1 said: Using consensus theorem (XY + X'Z + YZ = XY + X'Z) let L' = X let C = Y let I = Z Hence your expression becomes: XY + Z'Y + XZ rearrange as XZ + YZ' + XY Hence based on above theory XY is redundant: = XZ + YZ' i.e. = I'C + L'I So either I or you may have typing error. Click to expand... Hi If you do the truth table for every side of the equation; you will see that they are equal to each other; but I didn't succed to prove in in the terms of Boolean Algebra. thank you very much for your answer.
May 1, 2022 #6 andre_luis Super Moderator Staff member Joined Nov 7, 2006 Messages 9,595 Helped 1,190 Reputation 2,399 Reaction score 1,208 Trophy points 1,403 Location Brazil Activity points 55,686 Have you even tried the approach proposed in post #2? Upvote 0 Downvote
May 1, 2022 #7 A albbg Advanced Member level 4 Joined Nov 7, 2009 Messages 1,311 Helped 448 Reputation 898 Reaction score 409 Trophy points 1,363 Location Italy Activity points 9,985 As already said by std_match in post #2 the equation can't be correct. If you need an example simply let: I=0, C=1 and L=1 then LHS we have 0*1 + 1*1 + 0*0 = 1 RHS, intstead 0*1 + 0*0 = 0 Thus RHS <> LHS Possibly your equation contains a typo, please check it. Upvote 0 Downvote
As already said by std_match in post #2 the equation can't be correct. If you need an example simply let: I=0, C=1 and L=1 then LHS we have 0*1 + 1*1 + 0*0 = 1 RHS, intstead 0*1 + 0*0 = 0 Thus RHS <> LHS Possibly your equation contains a typo, please check it.