Dale - Computer Science Illuminated 128

Dale - Computer Science Illuminated 128 - Boolean algebra...

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Circuit equivalence The same output for each corresponding input- value combination for two circuits 4.4 Circuits 101 And once again, let’s complete our series of representations by expressing this circuit as a truth table. Like the previous example, since there are three input values there are eight rows in the truth table: Pick a row from this truth table and follow the logic of the circuit diagram to make sure the final results are consistent. Try it with a few rows to get comfortable with tracing the logic of a circuit. Now compare the final result column in this truth table to the truth table for the previous example. They are identical. We have therefore just demonstrated circuit equivalence . That is, both circuits produce the exact same output for each input value combination. In fact, this situation specifically demonstrates an important property of
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Unformatted text preview: Boolean algebra called the distributive law: A(B+C) = AB + AC That’s the beauty of Boolean algebra: It allows us to apply provable math-ematical principles to help us design logical circuits. The following chart shows a few of the properties of Boolean algebra: A 1 1 1 1 B 1 1 1 1 C 1 1 1 1 B + C 1 1 1 1 1 1 A(B+C) 1 1 1 Property AND Commutative Associative Distributive Identity Complement DeMorgan's law –7 0 7– .–7)C 0 –.7C) –.7 8 C) 0 .–7) 8 .–C) –> 0 – –.–2) 0 ! .–7)2 0 –2 OR 72 OR – 8 7 0 7 8 – .– 8 7) 8 C 0 – 8 .7 8 C) – 8 .7C) 0 .– 8 7).– 8 C) – 8 ! 0 – – 8 .–2) 0 > .– 8 7)2 0 –272...
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