UNIVERSAL GATES

Objectives What are gates? Fundamental gates. Universal gates - NAND and NOR. How to implement NOT, AND, and OR gates using NAND gates only. How to implement NOT, AND, and OR gates using NOR gates only. Equivalent gates. Two-level digital circuit implementations using universal gates only. Applications

What is a gate? Combination of transistors(circuit) that takes one or more inputs and generates an output. So called because one logic state enables or “gates” another logic state. For each gate, the symbol, the truth table, and the formula are shown.

NOT Gate A NOT gate accepts one input value and produces one output value

AND Gate An AND gate accepts two input signals If the two input values for an AND gate are both 1, the output is 1; otherwise, the output is 0

OR Gate If the two input values are both 0, the output value is 0; otherwise, the output is 1

Universal Gates A universal gate is a gate which can implement any Boolean function without using any other gate type. The NAND and NOR gates are universal gates. In practice, this is advantageous since NAND and NOR gates are economical and easier to fabricate and are the basic gates used in all IC digital logic families. In fact, an AND gate is typically implemented as a NAND gate followed by an inverter, not the other way around!!  Likewise, an OR gate is typically implemented as a NOR gate followed by an inverter, not the other way around!! 

NAND and NOR Gates The NAND and NOR gates are essentially the opposite of the AND and OR gates, respectively

Link inputs B & C together (to a same source). Universal Gates How to use NAND gates to build a NOT gate? Truth Table A Q C B A B C Q 1 Hint! Link inputs B & C together (to a same source). When A = 0, B = C = 0 When A = 1, B = C = 1

Universal Gates How to use NAND gates to build an AND gate? Truth Table A B C Q 1 NAND NOT A C Q B Hint 1 : Use 2 NAND gates Hint 2 : From a NAND gate, build a NOT gate Hint 3 : Put this “NOT” gate after the NAND gate

Hint 2 : Use 2 NAND gates to build 2 NOT gates Universal Gates How to use NAND gates to build an OR gate? Truth Table A B C D Q A B C D Q 1 Hint 1 : Use 3 NAND gates Hint 2 : Use 2 NAND gates to build 2 NOT gates Hint 3 : Put the 3rd NAND gate after the 2 “NOT” gates

Link inputs B & C together (to a same source). Universal Gates How to use NOR gate to build a NOT gate? Truth Table A B C Q 1 A Q B C Hint! Link inputs B & C together (to a same source). When A = 0, B = C = 0 When A = 1, B = C = 1

Universal Gates How to use NOR gates to build an OR gate? A B C D E Q Truth Table A B C D E Q 1 NOR NOT A D C Q B E Hint 1 : Use 2 NOR gates Hint 2 : From a NOR gate, build a NOT gate Hint 3 : Put this “NOT” gate after a NOR gate

Hint 2 : From 2 NOR gates, build 2 NOT gates Universal Gates How to use NOR gates to build an AND gate? Truth Table A B C D Q 1 A B C D Q Hint 1 : Use 3 NOR gates Hint 2 : From 2 NOR gates, build 2 NOT gates Hint 3 : Each “NOT” gate is an input to the 3rd NOR gate

Hint 2 : Use 3 NAND gates to build an OR gate Universal Gates How to use NAND gates to build a NOR gate? Truth Table A B C D Q E A B C D E Q 1 Hint 1 : Use 4 NAND gates Hint 2 : Use 3 NAND gates to build an OR gate Hint 3 : Use a NOR gate to build a NOT gate Hint 4 : Put the “NOT” gate after “OR” gate

Universal Gates How to use NOR gates to build a NAND gate? A B C D E Q Truth Table A B C D E Q 1 Hint 1 : Use 4 NOR gates Hint 2 : Use 3 NOR gates to build a NAND gate Hint 3 : Use the 4th NOR gate to build a NOT gate Hint 4 : Insert “NOT” gate after “NAND” gate

Equivalent Gates A NAND gate is equivalent to an inverted-input OR gate. A NOR gate is equivalent to an inverted-input AND gate.

Two-Level Implementations Boolean functions in either SOP or POS forms can be implemented using 2-Level implementations. For SOP forms AND gates will be in the first level and a single OR gate will be in the second level. For POS forms OR gates will be in the first level and a single AND gate will be in the second level. Using inverters to complement input variables is not counted as a level. SOP forms can be implemented using only NAND gates, while POS forms can be implemented using only NOR gates.

Example 1: Implement the following SOP function F = XZ + Y’Z + X’YZ

Example 2: Implement the following POS function  F = (X+Z) (Y’+Z) (X’+Y+Z)

Applications: Used in manufacturing logic circuits(devices such as multiplexers, registers, ALUs. Flash memory

Questions?? Why are NAND and NOR called universal gates? How many NAND gates make an AND gate? How many NOR gates make an OR gate? An inverted input OR gate is a ……………... Gate. POS forms can be implemented using ………. Gates.

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