Unit 7 Multi-Level Gate Circuits / NAND and NOR Gates

1. Unit 7Multi-Level Gate Circuits / NAND and NOR Gates Ku-Yaw Chang canseco@mail.dyu.edu.tw Assistant Professor, Department of Computer Science and Information Engineering Da-Yeh University

2. Contents • 7.1 Multi-Level Gate Circuits • 7.2 NAND and NOR Gates • 7.3 Design of Two-Level Circuits Using NAND and NOR Gates • 7.4 Design of Multi-Level NAND and NOR Gate Circuits • 7.5 Circuit Conversion Using Alternative Gate Symbols • 7.6 Design of Two-Level, Multiple-Output Circuits • 7.7 Multiple-Output NAND and NOR Circuits Fundamentals of Logic Design

3. 7.4 Design of Multi-Level NAND- and NOR-Gates Circuits • Multi-Level NAND-gate circuits • Simplify the switching function to be realized. • Design a multi-level circuit of AND and OR gates. The output gate must be OR. AND-gate outputs cannot be used as AND-gate inputs; OR-gate outputs cannot be used as OR-gate inputs. • Number the levels starting with the output gate as level 1. Replace all gates with NAND gates, leaving all interconnections between unchanged. Leave the inputs to levels 2, 4, 6, …unchanged. Invert any literals which appear as inputs to levels 1, 3, 5,… Fundamentals of Logic Design

4. Multi-Level NAND-gate circuits Fundamentals of Logic Design

5. Contents • 7.1 Multi-Level Gate Circuits • 7.2 NAND and NOR Gates • 7.3 Design of Two-Level Circuits Using NAND and NOR Gates • 7.4 Design of Multi-Level NAND and NOR Gate Circuits • 7.5 Circuit Conversion Using Alternative Gate Symbols • 7.6 Design of Two-Level, Multiple-Output Circuits • 7.7 Multiple-Output NAND and NOR Circuits Fundamentals of Logic Design

6. 7.5 Circuit Conversion Using Alternative Gate Symbols • An inverter can be represented by • Inversion bubble • At the input • At the output Fundamentals of Logic Design

7. Alternative Gate Symbols • AND, OR, NAND, and NOR gates • Based on DeMorgan’s law Fundamentals of Logic Design

8. Alternative Gate Symbols • Why alternative symbols? • Facilitate the analysis and design of NAND and NOR gate circuits Fundamentals of Logic Design

9. NAND Gate Circuit Conversion Fundamentals of Logic Design

10. Conversion to NOR Gates Fundamentals of Logic Design

11. Conversion of AND-OR Circuit to NAND Gates • Convert all AND gates to NAND gates • Adding an inversion bubble at the output • Convert all OR gates to NAND gates • Adding inversion bubbles at the inputs • An inverted output drives an inverted input • No further action Fundamentals of Logic Design

12. Conversion of AND-OR Circuit to NAND Gates • A non-inverted gate output drives an inverted gate input or vice versa • Insert an inverter • A variable drives an inverted input • Complement the variable Fundamentals of Logic Design

13. Conversion of AND-OR Circuit to NAND Gates Fundamentals of Logic Design

14. Contents • 7.1 Multi-Level Gate Circuits • 7.2 NAND and NOR Gates • 7.3 Design of Two-Level Circuits Using NAND and NOR Gates • 7.4 Design of Multi-Level NAND and NOR Gate Circuits • 7.5 Circuit Conversion Using Alternative Gate Symbols • 7.6 Design of Two-Level, Multiple-Output Circuits • 7.7 Multiple-Output NAND and NOR Circuits Fundamentals of Logic Design

15. 7.6 Design of Two-Level, Multiple-Output Circuits • The realization of several functions of the same variables • A more economical realization Fundamentals of Logic Design

16. Multi-Output Function • Given Functions F1(A, B, C, D) = ∑ m(11, 12, 13, 14, 15) F2(A, B, C, D) = ∑ m(3, 7, 11, 12, 13, 15) F3(A, B, C, D) = ∑ m(3, 7, 12, 13, 14, 15) Fundamentals of Logic Design

17. Separate Realizations Fundamentals of Logic Design

18. Multiple-Output Simplification • F1 = AB + ACDF2 = ABC’ + CD F3 = A’CD + AB • AB: F1 and F3 • CD (F2) can be replaced by A’CD + ACD • F2 = ABC’ + A’CD + ACD Fundamentals of Logic Design

19. Multiple-Output Realization Fundamentals of Logic Design

20. Comparison Fundamentals of Logic Design

21. Multiple-Output Simplification • If several solutions are available • Try to minimize the total number of gates required • Choose the one with minimum gates inputs Fundamentals of Logic Design

22. Contents • 7.1 Multi-Level Gate Circuits • 7.2 NAND and NOR Gates • 7.3 Design of Two-Level Circuits Using NAND and NOR Gates • 7.4 Design of Multi-Level NAND and NOR Gate Circuits • 7.5 Circuit Conversion Using Alternative Gate Symbols • 7.6 Design of Two-Level, Multiple-Output Circuits • 7.7 Multiple-Output NAND and NOR Circuits Fundamentals of Logic Design

23. 7.7 Multiple-Output NAND and NOR Circuits Fundamentals of Logic Design

24. Homework #1 • 7.17 • 7.19 • 7.20 • 7.25 • 7.26 • 7.1 • 7.3 • 7.4 • 7.8 • 7.10 Paper Submission, due on March 22, 2004. Late submission will not be accepted. Fundamentals of Logic Design