The compliment of the function expressed in terms of sum of min terms can be obtained by taking sum of missing min terms in the original functions e.g. f= ∑(4, 5, 7) = m7 + m5 + m4 Its compliment is f’ = ∑(0, 1, 2, 3, 6) = m0 + m1 + m2 + m3 + m6 The compliment […]
Boolean Algebra
Boolean Equations: Different forms
Standard form: In a standard form we don’t have to compulsorily write all the literals in all the terms of an expression. e.g. f = xyz + y + x f = x’y’z’ + x’yz f= xy + x’y’ Canonical form: In a canonical form we have to compulsorily write all the literals in all the terms […]
Consensus Theorem
Consensus theorem: Given a pair of terms for which a variable appears in one term and its compliment in the other term then consensus term is formed by ANDing the original terms together leaving out the selected variable and its compliment. e.g. Find consensus term out of the two terms X.Y & X’.Z […]
Boolean algebra laws
There are following laws in Boolean algebra: Associative Law: This law states that if we have 3 variables x, y, z then X*(Y*Z) = (X*Y)*Z Commutative Law: This law states that X*Y = Y*X Identity element: If e is the identity then we have the relation with the Boolean algebra e*x = x*e=x Hence 0 is identity for […]
Logic Gates
Following are the basic logical operations which we can operate on binary variables: AND: This operation is represented by dot (.) If we two binary variables as x and y then we can represent AND operation by z=x.y and resultant of the operations is also a binary variable. Following table represents result of AND of every […]
Binary Logic
Binary logic deals with variables which have two discrete values and those two values can be true or false, on or off, yes or no etc. But we think in terms of 1 & 0. Those variables are called binary variables. In digital circuits we represent the higher value by 3V to 5V and lower […]