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Boolean Functions, equivalent truth table and gate level implementation.
Operator precedence for evaluating Boolean Expressions.
Highest Parentheses
NOT
AND
Lowest OR
Boolean function example:
F1 = (x + y)z’
Where F1 is a Boolean function of binary variables and binary operators. The binary variables and operators are specified below
Binary variables = x, y and z
Binary operators = Parentheses, NOT, AND and OR
Solving or minimization of the functions are performed in a particular precedence shown below
Representation of Boolean function in Truth Table
The truth table above lists all the variables in function as inputs (x, y and z) and the output of function as column F1. In order to derive a gate level implementation we will need to analyze all possible combination of inputs and corresponding output.
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Next, we will discuss the equivalent gate level Implementation for Function F1. The circuit is most optimized implementation of the boolean function. F1 = (x + y)z’
