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ECE 301 – Digital Electronics

NAND-NAND and NOR-NOR Circuits and Even and Odd Logic Functions. ECE 301 – Digital Electronics. Logic Gates. AND and OR Gates 2-input gates realized with 6 CMOS transistors 3-input gates realized with 8 CMOS transistors NAND and NOR Gates 2-input gates realized with 4 CMOS transistors

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ECE 301 – Digital Electronics

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  1. NAND-NAND and NOR-NOR Circuits and Even and Odd Logic Functions ECE 301 – Digital Electronics

  2. ECE 301 - Digital Electronics Logic Gates • AND and OR Gates • 2-input gates realized with 6 CMOS transistors • 3-input gates realized with 8 CMOS transistors • NAND and NOR Gates • 2-input gates realized with 4 CMOS transistors • 3-input gates realized with 6 CMOS transistors • Therefore, it is more cost efficient to design logic circuits from NAND and NOR gates.

  3. ECE 301 - Digital Electronics Using the NAND Gate

  4. ECE 301 - Digital Electronics “Redrawing” the NAND Gate bubble denotes inversion Remember, this is an application of DeMorgan's Theorem

  5. ECE 301 - Digital Electronics Using the NOR Gate

  6. ECE 301 - Digital Electronics “Redrawing” the NOR Gate bubble denotes inversion Remember, this is an application of DeMorgan's Theorem

  7. ECE 301 - Digital Electronics SOP using NAND Gates • Converting from AND-OR to NAND-NAND • Draw the AND-OR logic circuit for the SOP expression. • Add bubbles (inversion) • At the output of each AND gate • At the corresponding inputs of the OR gate • Two bubbles on the same signal cancel (A'' = A) • All gates in the logic circuit are NAND gates • Two different representations for the NAND gate • 74xx08 Quad 2-input NAND Gate

  8. ECE 301 - Digital Electronics NAND Gate Realization of SOP

  9. ECE 301 - Digital Electronics NAND Gate Realization of SOP

  10. ECE 301 - Digital Electronics NAND Gate Realization of amultilevel AND-OR Circuit

  11. ECE 301 - Digital Electronics POS using NOR Gates • Converting from OR-AND to NOR-NOR • Draw the OR-AND logic circuit for the POS expression. • Add bubbles (inversion) • At the output of each OR gate • At the corresponding inputs of the AND gate • Two bubbles on the same signal cancel (A'' = A) • All gates in the logic circuit are NOR gates • Two different representations for the NOR gate • 74xx02 Quad 2-input NOR Gate

  12. ECE 301 - Digital Electronics NOR Gate Realization of POS Need to include (or draw on the board) the OR-AND circuit.

  13. ECE 301 - Digital Electronics NOR Gate Realization of POS Need to include (or draw on the board) the OR-AND circuit.

  14. ECE 301 - Digital Electronics Example: Implement the function F(A,B,C) = S m(0,2,3,7) using only NAND gates.

  15. ECE 301 - Digital Electronics Example: Implement the function F(A,B,C) = S m(0,2,3,7) using only NOR gates.

  16. ECE 301 - Digital Electronics Example: Implement the function F(A,B,C) = P M(1,5,6,7) using only NOR gates.

  17. ECE 301 - Digital Electronics Example: Implement the function F(A,B,C) = P M(1,5,6,7) using only NAND gates.

  18. ECE 301 - Digital Electronics Even and Odd Logic Functions

  19. ECE 301 - Digital Electronics Even and Odd Logic Functions Why is this an odd function? Why is this an even function?

  20. ECE 301 - Digital Electronics Even and Odd Logic Circuits

  21. ECE 301 - Digital Electronics Even and Odd Parity

  22. ECE 301 - Digital Electronics Parity Generator

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