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Logic Gates

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AND Function Output Y is TRUE if inputs A AND B are TRUE, else it is FALSE. Logic Symbol Text Description Truth Table Boolean Expression AND A B Y AND Symbol Y = A x B = A • B = AB

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OR Function Output Y is TRUE if input A OR B is TRUE, else it is FALSE. Logic Symbol Text Description Truth Table Boolean Expression A B Y OR OR Symbol Y = A + B

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**NOT Function (inverter)**

Output Y is TRUE if input A is FALSE, else it is FALSE. Y is the inverse of A. Text Description Logic Symbol A Y NOT Truth Table Y = A’ Alternative Notation Y = !A NOT Bar Boolean Expression Y = A

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NAND Function Output Y is FALSE if inputs A AND B are TRUE, else it is TRUE. Logic Symbol Text Description Truth Table Boolean Expression A bubble is an inverter This is an AND Gate with an inverted output A B Y NAND Y = A x B = AB

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NOR Function Output Y is FALSE if input A OR B is TRUE, else it is TRUE. Logic Symbol Text Description Truth Table Boolean Expression A bubble is an inverter. This is an OR Gate with its output inverted. A B Y NOR Y = A + B

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**Circuit-to-Truth Table Example**

OR A Y NOT AND B C A B C Y 2# of Inputs = # of Combinations 2 3 = 8

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**Circuit-to-Truth Table Example**

OR A Y NOT AND B C 1 A B C Y

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**Circuit-to-Truth Table Example**

OR A Y NOT AND B C 1 A B C Y

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**Circuit-to-Truth Table Example**

OR A Y NOT AND B C 1 A B C Y 1

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**Circuit-to-Truth Table Example**

OR A Y NOT AND B C 1 A B C Y 1

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**Circuit-to-Truth Table Example**

OR A Y NOT AND B C 1 A B C Y 1

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**Circuit-to-Truth Table Example**

OR A Y NOT AND B C 1 A B C Y 1

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**Circuit-to-Truth Table Example**

OR A Y NOT AND B C 1 A B C Y 1

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**Circuit-to-Truth Table Example**

OR A Y NOT AND B C 1 A B C Y 1

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**Circuit-to-Boolean Equation**

A B OR A Y NOT AND B C = A B + A C A 1 } 1 } A C A B C Y

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**A - O - I Logic AND Gates NAND - NAND Logic OR Gates NOR - NOR Logic**

Y NOT AND B C AND Gates Other Logic Arrangements: NAND - NAND Logic NOR - NOR Logic OR Gates INVERTER Gates

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**NAND Gate – Special Application**

S T A B Y NAND 1 Equivalent To An Inverter Gate

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**NOR Gate - Special Application**

S T A B Y NOR 1 Equivalent To An Inverter Gate

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1 EENG 2710 Chapter 2 Algebraic Methods For The Analysis and Synthesis of Logic circuits.

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