Boolean algebra

May 29th, 2015
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In mathematics and computer science, Boolean algebras, or Boolean lattices, are algebraic structures which "capture the essence" of the logical operations AND, OR and NOT as well as the set theoretic operations union,intersection and

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Boolean Algebra(The Mathematics of Circuit Design)Before we venture into the laws that govern Boolean Algebra we must remind ourselves that the:plus sign (+) means OR the multiplication sign () means ANDAs we work our way through the laws of Boolean Algebra we will see that these signs are appropriate.Commutative LawIn math classx+y = y+x[3+4 = 4+3]xy = yx[8x9 = 9x8]In Boolean AlgebraA+B = B+AAB = BAAssociative LawIn math class(x+y) + z = x+(y+z)[(3+4) + 5 = 3+(4+5)](xy) z = x(yz)[(8x9)x6 = 8x(9x6)]In Boolean Algebra(A+B) + C= A+(B+C)(AB) C = A(BC)Distributive LawIn math classx(y+z) = xy + xz[3x(4+5) = 3x4 + 3x5(multiplication can be distributed over addition)x+(yz) (x+y) (x+z)[3+(45) (3+4) (3+5)](addition cannot be distributed over multiplication)In Boolean AlgebraA(B+C) = (AB) + (AC)(AND can be distributed over OR)ABCB+CA (B+C)(AB)(AC)(AB) +( AC)0000000000110000010100000111000010000000101110111101110111111111A+(BC) = (A+B) (A+C)(OR can be distributed over AND)ABCBCA+ (BC)(A+B)(A+C)(A+B )(A+C)0000000000100010010001000111111110001111101011111100111111111111DeMorgan's LawsAND and OR logic are related by DeMorgan's LawsAB = A+BThe complemen

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