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# gates - Practicing Boolean gates Problem 1 Find the truth...

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Practicing Boolean gates Problem 1 Find the truth table for the following circuit: X Y Z X Y Z 0 0 1 0 1 0 1 0 1 1 1 1 Problem 2 Find the truth table for the following circuit: X Y Z X Y Z 0 0 0 0 1 1 1 0 0 1 1 1 Note that Z is always equal to Y. Therefore, this circuit can be simplified by directly connecting Y to Z with a wire (ignoring X). Problem 3 Find the truth table for the following circuit: X Y Z 1

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X Y Z 0 0 0 0 1 1 1 0 1 1 1 0 This behavior is known as the exclusive OR, XOR. If Z=X XOR Y, then Z is one if either X is 1 or Y is 1, but not both. In general, XOR produces a 1 if the number of 1’s in the inputs is odd (that’s why it is also called parity). The XOR logic is useful, so it was given a symbol: Problem 4 Given a truth table, find a circuit that produces it. X Y Z 0 0 1 0 1 1 1 0 0 1 1 1 We will illustrate the process step by step. 1. Identify all the rows in the truth table that have a 1 for the output (ignore the others): X Y Z 0 0 1 0 1 1 1 1 1 2. Say what you see in English using the every day logic:
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gates - Practicing Boolean gates Problem 1 Find the truth...

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