functional notation addendum to chapter 4. 2 logic notation systems we have seen three different,...
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Functional Notation
Addendum to Chapter 4
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Logic Notation Systems We have seen three different, but equally
powerful, notational methods for describing the behavior of gates and circuits: Boolean expressions logic diagrams truth tables
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Recall that… Boolean expressions are expressions in
Boolean algebra, a mathematical notation for expressing two-valued logic.
This algebraic notation is an elegant and powerful way to demonstrate the activity of electrical circuits.
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Recall further that… Logic diagram A graphical representation of
a circuitEach type of gate is represented by a specific graphical symbol.
Truth table A table showing all possible input value and the associated output values.
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A Fourth SystemI addition to these three, there is another widely
used system of notation for logic.
Functional Notation
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Functional Notation Uses a function name followed by a list of
arguments in place of the operators used in Boolean Notation.
For example: A’ becomes NOT(A)
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Functional EquivalentsBoolean Notation Functional Notation
X=A’ X=NOT(A)
X=A + B X=OR(A,B)
X=A B X=AND(A,B)
X=(A + B)’ X=NOT(OR(A,B))
X=(A B)’ X=NOT(AND(A,B))
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XORXOR must be defined in terms of the 3 logic
primitives: AND, OR, and NOTRecall its explanation:
“one or the other but not both”In Boolean Notation this becomes:
X=(A + B) (A B)’In Functional Notation:
X=AND(OR(A,B),NOT(AND(A,B)))
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XORThe truthtable for XOR
reveals a hint for simpliying or expression.
Note that XOR is false (0) when A and B are the same, and true (1) when they are different.
A B XOR0 0 0
0 1 1
1 0 1
1 1 0
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XORSo XOR can be expressed very simply as:
X=NOT(A=B)or
X=A<>B
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Consider this familiar circuit
X=(AB + AC)
How will this expression look in functinal notation?
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Equvalent expressions
X=(AB + AC) AND(A,B) AND(A,C)
X=OR(AND(A,B), AND(A,C))
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The equivalent circuit
X=A (B + C)X=AND(A, OR(B,C))