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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 Spring '09
 SaadMneimneh
 Boolean Algebra, Logic gate, exclusive or, XOR gate, 8 1bit

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