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DeMorgans Theoremsand

Real-life Applications of Logic Gates

Prepared by

Dr. Anu Gokhale

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DeMorgans Theorem

Reference: http://www.allaboutcircuits.com/vol_4/chpt_7/9.html

NOR gate equivalent

Draw an equivalent

one for a NOR gate

NAND gate equivalent

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Why Alternate Gates?

By use of De Morgan's theorem: AND function is identical to an OR function with negated inputs and outputs.

Likewise, an OR function is identical to an AND function with negated inputs and outputs.

Similarly, a NAND gate is equivalent to an OR gate with negated inputs, and

NOR gate is equivalent to an AND gate with negated inputs.

Any connection that has logic negations at both ends can be replaced by a negation-less connectionand a suitable change of gate or vice-versa. Any connection that has a negation at one end and nonegation at the other can be made easier to interpret by instead using the De Morgan equivalentsymbol at either of the two ends. When negation or polarity indicators on both ends of a connectionmatch, there is no logic negation in that path (effectively, bubbles "cancel"), making it easier tofollow logic states from one symbol to the next. This is commonly seen in real logic diagrams - thusthe reader must not get into the habit of associating the shapes exclusively as OR or AND shapes,but also take into account the bubbles at both inputs and outputs in order to determine the "true"logic function indicated.

All logic relations can be realized by using NAND gates (this can also be done usingNOR gates). De Morgan's theorem is most commonly used to transform all logicgates to NAND gates or NOR gates. This is done mainly since it is easy to buy logicgates in bulk and because many electronics labs stock only NAND and NOR gates.

References: Digital Systems by Tocci, and others

http://en.wikipedia.org/wiki/File:7400.jpg

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Clothes Dryer

The power switch must be turned on and door

must be shut for the dryer to turn on

What are the inputs?

Whats the output?

Which logic gate should be used?

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Computer Monitor

The monitor screen blanks out if either the

keyboard or the mouse in inactive for 15

seconds

What are the inputs?

Whats the output?

Which logic gate should be used?

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More Applications online

http://www.allaboutcircuits.com/vol_4/chpt_7/9.html

http://www.brighthubengineering.com/diy-

electronics-devices/3595-and-nand-and-not-logic-gates-explained/

http://www.cs.brown.edu/~jes/book/pdfs/ModelsOfC

omputation_Chapter2.pdf

http://computer.howstuffworks.com/boolean6.htm

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