ELEC 2200-002 Digital Logic Circuits Fall 2008 Logic Synthesis (Chapters 2-5)

1. ELEC 2200-002Digital Logic CircuitsFall 2008Logic Synthesis (Chapters 2-5) Vishwani D. Agrawal James J. Danaher Professor Department of Electrical and Computer Engineering Auburn University, Auburn, AL 36849 http://www.eng.auburn.edu/~vagrawal vagrawal@eng.auburn.edu ELEC2200-002 Lecture 6

2. Logic Synthesis • Definition: To design a logic circuit such that it meets the specifications and can be economically manufactured: • Performance – meets delay specification, or has minimum delay. • Cost – uses minimum hardware, smallest chip area, smallest number of gates or transistors. • Power – meets power specification, or consumes minimum power. • Testablility – has no redundant (untestable) logic and is easily testable. ELEC2200-002 Lecture 6

3. Synthesis Procedure • Minimization – Obtain MSOP or MPOS. This is also known as two-level minimization because the result can be implemented as a two-level AND-OR or NAND-NAND or NOR-NOR circuit. • Technology mapping – Considering design requirements, transform the minimized form into one of the technologically realizable forms: • Programmable logic array (PLA) • Standard cell library • Field programmable gate array (FPGA) • Other . . . ELEC2200-002 Lecture 6

4. References on Synthesis • G. De Micheli, Synthesis and Optimization of Digital Circuits, New York: McGraw-Hill, 1994. • S. Devadas, A. Ghosh and K. Keutzer, Logic Synthesis, New York: McGraw-Hill, 1994. ELEC2200-002 Lecture 6

5. Programmable Logic Array (PLA) • A direct implementation of multi-output function as a two-level circuit in MOS technology. • PLA styles: • NAND-NAND • NOR-NOR • Textbook, Chapter 5. ELEC2200-002 Lecture 6

6. Example: Two-Output Function Need four products: P1, P2, P3, P4 F1 A F2 A D D C C B B ELEC2200-002 Lecture 6

7. Two-Level AND-OR Implementation • Also known as technology-independent circuit. INPUTS AND OR C P1 F1 P2 A P3 F2 B P4 D ELEC2200-002 Lecture 6

8. NAND-NAND Implementation INPUTS NAND NAND C F1 A F2 B D ELEC2200-002 Lecture 6

9. A NAND Gate in MOS Technology VDD VDD VDD XY XY XY X X X Y Y Y GND GND GND R. C. Jaeger and T, N. Blalock, Microelectronic Circuit Design, Boston: McGraw-Hill, 2008, Section 6.8.2. ELEC2200-002 Lecture 6

10. NAND-NAND PLA A B C D F1 F2 VDD VDD VDD VDD VDD VDD GND ELEC2200-002 Lecture 6

11. NAND-NAND PLA SCHEMATIC A B C D F1 F2 INPUTS OUTPUTS AND-plane OR-plane ELEC2200-002 Lecture 6

12. Standard-Cell Design • Obtain two-level minimized form. • Map the design onto predesigned building blocks called standard cells (technology mapping). • Standard-cell library contains predesigned logic cells in the technology of manufacture. Examples of technology: • 90 nanometer CMOS • 65 nanometer CMOS • 45 nanometer CMOS • . . . • This is known as application-specific integrated circuit (ASIC). ELEC2200-002 Lecture 6

13. Technology Mapping • Find a common logic elements, e.g., two-input NAND gate and inverter. • MSOP is converted into NAND-NAND circuit. • Split gates into library cells, two-input NAND gates and inverters. • Cover the circuit with standard cells, also split into two-input NAND gates and inverters (graph-matching). ELEC2200-002 Lecture 6

14. A Typical Cell Library S. Devadas, A. Ghosh and K. Keutzer, Logic Synthesis, New York: McGraw-Hill 1994, Section 7.7, pp. 185-198. ELEC2200-002 Lecture 6

15. NAND3 Cell Directed Acyclic Graph (DAG) (tree) ELEC2200-002 Lecture 6

16. NAND4 Cell ELEC2200-002 Lecture 6

17. AOI21 Cell ELEC2200-002 Lecture 6

18. OAI21 Cell ELEC2200-002 Lecture 6

19. AOI22 Cell ELEC2200-002 Lecture 6

20. XOR Cell ELEC2200-002 Lecture 6

21. Technology Mapping Procedure • Obtain MSOP. • Convert to two-level AND-OR circuit. • Transform to two-level NAND-NAND circuit. • Transform to two-input NAND and inverter tree network. • Perform an optimal pattern matching to obtain a minimum cost tree covering. ELEC2200-002 Lecture 6

22. Previous Example: 2-Level NAND INPUTS NAND NAND C F1 A F2 B D ELEC2200-002 Lecture 6

23. Circuit is a Directed Acyclic Graph (DAG) C F1 A F2 B Each node is a NAND gate. D ELEC2200-002 Lecture 6

24. Splitting into a Forest of Trees C F1 D B C D A F2 B A D ELEC2200-002 Lecture 6

25. Splitting DAG into Trees (Forest) C D F1 C B D A B F2 A D ELEC2200-002 Lecture 6

26. A Simple Technology Mapping NAND2 (3) NAND2 (3) C (2) F1 D B C D NAND3 (4) NAND3 (4) A F2 B (2) A Cost = 24 D NAND2 (3) ELEC2200-002 Lecture 6

27. Two-Input NAND Trees C F1 D B C D A F2 B A D ELEC2200-002 Lecture 6

28. Alternatively, in Graph Format C D F1 B C D A F2 B A D ELEC2200-002 Lecture 6

29. An Improved Technology Mapping C OAI21 (4) D (2) F1 Inverter inserted For pattern matching B NAND3 (4) C D NAND3 (4) A F2 B (2) NAND2 (3) A Cost = 22 D NAND2 (3) ELEC2200-002 Lecture 6

30. Alternatively, in Graph Format C OAI21 (4) D F1 (2) Inverter inserted For pattern matching B NAND3 (4) C D NAND3 (4) NAND2 (3) A F2 B (2) A D NAND2 (3) Cost = 22 ELEC2200-002 Lecture 6

31. Original Reference • K. Keutzer, “DAGON: Technology Binding and Local Optimization by DAG matching,” Proc.24th Design Automation Conf., 1987, pp. 341-347. ELEC2200-002 Lecture 6