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Lecture_6

# Lecture_6 - ECE 331 Digital System Design Boolean Algebra...

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ECE 331 – Digital System Design Boolean Algebra, Truth Tables, and Logic Function (Circuit) Simplification

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ECE 331 - Digital System Design 2 Message from an Author “The method which you use to get your answer is very important in this unit. If it takes you two pages of algebra and one hour of time to work a problem that can be solved in 10 minutes with three lines of work, you have not learned the material of this unit! Even if you get the correct answer, your work is not satisfactory if you worked the problem by an excessively long and time-consuming method. It is important that you learn to solve simple problems in a simple manner – otherwise, when you are asked to solve a complex problem, you will get bogged down and never get the answer.”
ECE 331 - Digital System Design 3 Boolean Algebra Used to study the logic design of digital circuits. Digital circuits are composed of two-state devices (e.g. transistors) that switch between one state and the other. Interested in the application of Boolean Algebra to switching circuits. Switching Algebra : A special case of Boolean Algebra in which all variables take on just two distinct values (0 or 1).

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ECE 331 - Digital System Design 4 Basic Logic Operations AND OR NOT (Complement) Order of Precedence 1. NOT 2. AND 3. OR - can be modified using parenthesis
ECE 331 - Digital System Design 5 Additional Logic Operations NAND - F = (A . B)' NOR - F = (A + B)' XOR - Output is 1 iff either input is 1, but not both. XNOR (aka. Equivalence) - Output is 1 iff both inputs are 1 or both inputs are 0.

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ECE 331 - Digital System Design 6 Boolean Expressions Composed of Literals – variables and their complements Logical operations Evaluated by Substituting a 0 or 1 for each literal Calculating the logical value of the expression A Truth Table specifies the value of the Boolean expression for every combination of the variables in the Boolean expression. For an n-variable Boolean expression, the truth table has 2 n rows (one for each combination).
ECE 331 - Digital System Design 7 Boolean Expressions T wo Boolean expressions are equivalent if they have the same value for each combination of the variables in the Boolean expression.

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Lecture_6 - ECE 331 Digital System Design Boolean Algebra...

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