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DeMorgan’s Theorems and Real-life Applications of Logic Gates

DeMorgan’s Theorems and Real-life Applications of Logic Gates. Prepared by Dr. Anu Gokhale. DeMorgan’s Theorem. NAND gate equivalent. NOR gate equivalent Draw an equivalent one for a NOR gate. Reference: http://www.allaboutcircuits.com/vol_4/chpt_7/9.html. Why Alternate Gates?.

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DeMorgan’s Theorems and Real-life Applications of Logic Gates

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  1. DeMorgan’s Theorems and Real-life Applications of Logic Gates Prepared by Dr. Anu Gokhale

  2. DeMorgan’s Theorem NAND gate equivalent NOR gate equivalent Draw an equivalent one for a NOR gate Reference: http://www.allaboutcircuits.com/vol_4/chpt_7/9.html

  3. Why Alternate Gates? • By use of De Morgan's theorem: • ANDfunction 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 connection and a suitable change of gate or vice-versa. Any connection that has a negation at one end and no negation at the other can be made easier to interpret by instead using the De Morgan equivalent symbol at either of the two ends. When negation or polarity indicators on both ends of a connection match, there is no logic negation in that path (effectively, bubbles "cancel"), making it easier to follow logic states from one symbol to the next. This is commonly seen in real logic diagrams - thus the 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 using NOR gates). De Morgan's theorem is most commonly used to transform all logic gates to NAND gates or NOR gates. This is done mainly since it is easy to buy logic gates in bulk and because many electronics labs stock only NAND and NOR gates. References: Digital Systems by Tocci, and others

  4. Clothes Dryer • The power switch must be turned on and door must be shut for the dryer to turn on • What are the inputs? • What’s the output? • Which logic gate should be used?

  5. Computer Monitor • The monitor screen blanks out if either the keyboard or the mouse in inactive for 15 seconds • What are the inputs? • What’s the output? • Which logic gate should be used?

  6. 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/ModelsOfComputation_Chapter2.pdf • http://computer.howstuffworks.com/boolean6.htm

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