copyright 2013, 2010, 2007, pearson, education, inc. section 3.7 switching circuits
TRANSCRIPT
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Section 3.7
Switching Circuits
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
What You Will Learn
Switching circuits
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Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Electrical CircuitsElectrical circuits can be expressed as logical statements.
T (true) represents a closed switch (or current flow).
F (false) represents an open switch (or no current flow).
In a series circuit the current can take only one path.
In a parallel circuit there are two or more paths the current can take.
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Series Circuit
Case 1: Both switches are closed; that is, p is T and q is T. The light is on, T.
Case 2: Switch p is closed and switch q is open; that is, p is T and q is F. The light is off, F.
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Series Circuit
Case 3: Switch p is open and switch q is closed; that is, p is F and q is T. The light is off, F.
Case 4: Both switches are open; that is, p is F and q is F. The light is off, F.
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Series Circuit
Switches in series will always be represented with a conjunction . ⋀In summary,
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Parallel Circuit
Case 1: Both switches are closed; that is, p is T and q is T. The light is on, T.
Case 2: Switch p is closed and switch q is open; that is, p is T and q is F. The light is on, T.
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Parallel Circuit
Case 3: Switch p is open and switch q is closed; that is, p is F and q is T. The light is on, T.
Case 4: Both switches are open; that is, p is F and q is F. The light is off, F.
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Parallel Circuit
Switches in parallel will always be represented with a disjunction .⋁In summary,
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Example 2: Representing a Switching Circuit with Symbolic Statementsa. Write a symbolic statement that represents the circuit.
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p and q are in parallel: p ⋁ q q and r are in series: q ⋀ rtogether we get: (p q⋀ ) ⋁ (q ⋀ r)
Example 2: Representing a Switching Circuit with Symbolic StatementsSolution
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Example 2: Representing a Switching Circuit with Symbolic Statements
b. Construct a truth table to determine when the light will be on.
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Example 2: Representing a Switching Circuit with Symbolic StatementsSolution
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Example 3: Representing a Symbolic Statement as a Switching CircuitDraw a switching circuit that represents
[(p ~⋀ q) (⋁ r ⋁ q)] ⋀s.
Solution
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Equivalent Circuits
Equivalent circuits are two circuits that have equivalent corresponding symbolic statements.
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Equivalent Circuits
Sometimes two circuits that look very different will actually have the exact same conditions under which the light will be on.The truth tables have identical answer columns.
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Example 4: Are the Circuits Equivalent?Determine whether the two circuits are equivalent.
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Example 4: Are the Circuits Equivalent?
p (⋁ q ⋀ r)
(p ⋁ q) (⋀ p ⋁ r)
Solution
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Example 4: Are the Circuits Equivalent?
The answer columns are identical.
Solution
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Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 4: Are the Circuits Equivalent?
Therefore, p (⋁ q ⋀ r) is equivalent to (p ⋁ q) (⋀ p ⋁ r) and the two circuits are equivalent.
Solution
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