Functional Notation

Functional Notation - Boolean Notation Functional Notation...

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Functional Notation Addendum to Chapter 4
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2 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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3 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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4 Recall further that… Logic diagram A graphical representation of a circuit Each 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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5 A Fourth System I addition to these three, there is another widely used system of notation for logic. Functional Notation
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6 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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7 Functional Equivalents
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Unformatted text preview: Boolean 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)) 8 XOR XOR must be defined in terms of the 3 logic primitives: AND, OR, and NOT Recall 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))) 9 XOR The 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 XOR 1 1 1 1 1 1 10 XOR So XOR can be expressed very simply as: X=NOT(A=B) or X=A<>B 11 Consider this familiar circuit X=(AB + AC) How will this expression look in functinal notation? 12 Equvalent expressions X= ( AB + AC ) AND(A,B) AND(A,C) X= OR( AND(A,B) , AND(A,C) ) Page 99 13 The equivalent circuit X=A (B + C) X=AND(A, OR(B,C))...
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This note was uploaded on 07/16/2010 for the course CSE CSE 1520 taught by Professor Paul during the Spring '09 term at York University.

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Functional Notation - Boolean Notation Functional Notation...

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