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Logic and Integrated Circuits

Logic and Integrated Circuits. Lin Zhong ELEC101, Spring 2011. Key concepts. Binary numeral system Boolean logic Logic gates Functional completeness CMOS gates Integrated circuits. Binary computing. Modern computing are based on binary states

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Logic and Integrated Circuits

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  1. Logic and Integrated Circuits Lin Zhong ELEC101, Spring 2011

  2. Key concepts • Binary numeral system • Boolean logic • Logic gates • Functional completeness • CMOS gates • Integrated circuits

  3. Binary computing • Modern computing are based on binary states • Two values: HIGH vs. LOW, 1 vs. 0, true vs. false • Why • Easy to implement • Robust against interference, noise,

  4. Computing with binary states • Binary numeral system • Represent numeric values using two values: 0 and 1 • The more “natural” numeral system is decimal • 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 • One to one mapping between the two systems

  5. Recall the single-input computer • Inverter Out In

  6. How about a two-to-one computer Binary “states” for input and output: HIGH or LOW (1 or 0) A Out B How many different computers are there?

  7. How about a two-to-one computer Binary “states” for input and output: HIGH or LOW (1 or 0) A Out B Useless ones: Out always 1; Out always 0; Out=A; Out=B Inverter Out= Invert (A); Out= Invert (B) Useful ones:????

  8. Three basic logic operations • Inversion (NOT): Out = ¬ In • AND: Out = A Λ B • OR: Out = A V B

  9. More gates • NAND • NOR • XOR • A XOR B = [A Λ (¬B)] V [(¬A) Λ B]

  10. How about a two-to-one computer Binary “states” for input and output: HIGH or LOW (1 or 0) A Out B Useless ones: Out = 0; Out =1; Out =A; Out=B; Inverters: Out= ¬A; Out= ¬B; Useful ones: Out = A Λ B(AND), Out= A V B(OR), Out= A XOR B Out = ¬(A Λ B) (NAND), Out= ¬ (A V B) (NOR), Out = ¬ ( A XOR B) A Λ (¬B); (¬A) Λ B; A V (¬B); (¬A)V B;

  11. Functional completeness • NOT, AND and OR can be used to build ANY Boolean function • Functionally complete • Can you prove the following? • NOR is functionally complete • NAND is functionally complete

  12. CMOS gates implementation • NOT • AND • OR

  13. CMOS gates: NAND Gnd

  14. CMOS gates: NOR Vdd A B Out Gnd

  15. Lab: NAND gate

  16. Adder A B A, B, and Sum are states that take value from 0 to 9 Carry-out is a state that take value from 0 to 1 Carry-out Sum

  17. The simplest adder A, B, and Sum are states that take value from 0 to 1 Carry-out is a state that take value from 0 to 1 A B Carry-out Truth table Sum

  18. The simplest adder (Contd.) A, B, and Sum are states that take value from 0 to 1 Carry-out is a state that take value from 0 to 1 A B Carry-out Truth table Sum Sum= A XOR B Carry-out = A AND B

  19. How many transistors do you need? Carry-out Sum= A XOR B Carry-out = A AND B Sum

  20. AND

  21. XOR • Sum= A XOR B = [A Λ (¬B)] V [(¬A) Λ B] • = [A AND (NOT B)] OR [(NOT A) AND B] • =[A NAND (NOT B)] NAND [(NOT A) NAND B] • = [(A AND B) NOR (A NOR B)]

  22. XOR (Contd.) Out

  23. XOR (Contd.) Vdd Out

  24. Computing with binary states (Contd.) • Boolean logic • Variables are binary (0 or 1) • Three operations on binary variables • Inversion (¬), AND (Λ), and OR (V) • Five axioms George Boole 1815-1864

  25. Integrated Circuit Shared Nobel Prize in Physics 2000

  26. Photolithography

  27. 1969

  28. Ivan Sutherland won Turing Award in 1988 for his Ph.D. work in 1963 http://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-574.pdf

  29. “Programmable” integrated circuit A B Carry-out Sum

  30. “Programmable” integrated circuit A B Control Output

  31. “Programmable” integrated circuit Storage A B Control Output

  32. “Programmable” integrated circuit Storage A B Control Output

  33. “Programmable” integrated circuit Storage A B Instruction in machine code 0110100010101 Control Output

  34. “Programmable” integrated circuit Storage A B Control Default start instruction Output

  35. Computing vs. human performance Sources: intel.com and factmonster.com

  36. Computing vs. humanity Source: Intel.com and dol.gov

  37. Computing: 60 years ago Wiring ENIAC with a new program http://ftp.arl.army.mil/ftp/historic-computers/png/eniac4.png

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