Boolean Expression:Consider a Boolean algebra (B, ∨,∧,',0,1).A Boolean expression over Boolean algebra B is defined as
Example: Consider a Boolean algebra ({0, 1, 2, 3},∨,∧,',0,1).
are Boolean expressions over the Boolean Algebra. A Boolean expression that contains n distinct variables is usually referred to as a Boolean expression of n variables. Evaluation of Boolean Expression:Let E (x1,x2,....xn)be a Boolean Expression of n variables over a Boolean algebra B. By an assignment of values to the variables x1,x2,....xn, means an assignment of elements of A to be the values of the variables. We can evaluate the expression E ( x1,x2,....xn) by substituting the variables in the expression by their values. Example: Consider the Boolean Expression E( x1,x2,x3)=(x1∨ x2 )∧(x1∨ x2 )∧(x2∨ x3) over the Boolean algebra ({0,1}, ∨,∧,') By assigning the values x1=0,x2=1,x3=0 yields E (0, 1, 0) = (0∨1)∧(0∨1)∧(1∨0)=1∧1∧0=0. Equivalent Boolean Expressions:Two Boolean expressions of n variables are said to be equal if they assume the same value for every assignment of values to the n variables. Example: The following two Boolean algebras (x1∧x2)∨(x1∧ x3 ) and x1∧ (x2∨ x3) are equivalent. We may write E1( x1,x2,....xn)=E2( x1,x2,....xn) to mean the two expressions E1( x1,x2,....xn) and E2( x1,x2,....xn)are equivalent. Example: The Boolean expression (x1∧x2∧x3)∨(x1∧x2 )∨(x1∧x3) over the Boolean algebra ({0, 1}, ∨,∧,') defines the function f in figure. Min-term: A Boolean Expression of n variables x1,x2,....xn is said to be a min-term if it is of the form x1∧x2∧x3∧....∧xn where xi is used to denote xi or xi'. Next TopicCanonical Forms |