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Rathika i bca

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Rathika i bca

  1. 1. BOOLEANALGEBRADEFINITIONS: Boolean algebra is in fact an algebric structure defined ona set of elements with two binary operators ‘+’ and ‘.’Provided the following postulates are satisfied. A. (a) closure with respect to the operator ‘+’. (b) closure with respect to the operator ‘.’ . B. (a) an identity element with respect to ‘+’ designated x+0=0+x=x (c) an identity element with respect to ‘.’ Designated x.1=1.x=xFUNDAMENTALS OF BOOLEANALGEBRA: The variables used in Boolean equationhave unique characteristics and assume onlyone of the two possible values , i.e. either a 1 ora 0.The following rules of logical addition,multiplication, negation also define the ORgate And and NOT operations respectively.LOGICAL ADDITION: 0+0=0 OR operations: 0+1=1 1+0=1 x y x+y
  2. 2. 1+1=1 0 0 0 0 1 1 1 0 1 1 1 1LOGICAL MULTIPLICATIONS: 0.0=0 0.1=0 1.0=0 1.1=1AND operation x y x.y 0 0 0 0 1 0 1 0 0 1 1 1Logical negation 1’=0 0’=1NOT operations: X x’ 1 0 0 1 1

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