laws (theorems) of boolean algebra laws of complementation othe term complement means, to invert or...
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Laws (Theorems) of Boolean algebra
Laws of Complementationo The term complement means, to invert or to
change 1's to 0's and 0's to 1's, for which purpose inverters or NOT gates are used.
o A complement of a variable is represented by a bar over the letter. For example, the complement of a variable A will be denoted by A
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QUESTION PAPERS 1
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Law 1: = 1
Law 2: = 0
Law 3: If A = 0,
Law 4: If A = 1,
Law 5:
0
1
1A
0A
AA
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QUESTION PAPERS 2
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AND Laws
• Law 6: A.0=0
• Law 7: A.1=A
• Law 8: A.A=A
• Law 9: 0. AA
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QUESTION PAPERS 3
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OR Laws
• Law 10: A +0 = A
• Law 11: A +1 = 1
• Law 12: A +A = A
• Law 13: 1 AA
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QUESTION PAPERS 4
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Commutative Laws
– This states that the order in which the variables are OR’ed and AND’ed will make no difference in the output.
• Law14: A. B = B. A• Law 15 : A + B = B + A
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QUESTION PAPERS 5
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Associative Laws
This law states that the order in which the variables are grouped will not make any difference in the output.
• Law 16: A + (B + C) = (A + B) + C
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QUESTION PAPERS 6
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• Law 17: A.(B.C) = (A.B).C
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QUESTION PAPERS 7
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Distributive LawsThese laws allow the factoring or multiplying out of
expressions.
• Law 18: A .(B +C) = (A .B) + (A .C)• Law 19: A + (B .C) = (A + B) (A + C)
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QUESTION PAPERS 8
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De Morgan's Theorems
• 1.
• 2.
• The complement of any Boolean expression is found by using these two rules.
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QUESTION PAPERS 9
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Steps for complementation:
• 1. Replace ‘+’ symbols with ‘.’ symbols and ‘.’ symbols with ‘+’ symbols.
• 2. Complement each term.
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QUESTION PAPERS 10
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Proof of De Morgan's Theorems
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QUESTION PAPERS 11
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QUESTION PAPERS 12