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 2

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, 3

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 4 DecimalBinary 00 11 210 311 4100 DecimalBinary 5101 6110 7111 81000 91001

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

6. How about a two-to-one computer 6 Binary “states” for input and output: HIGH or LOW (1 or 0) How many different computers are there? A Out B AB 00 01 10 11

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

8. Three basic logic operations Inversion (NOT): Out = ¬ In AND: Out = A Λ B OR: Out = A V B 8 InOut 01 10 AB 000 010 100 111 AB 000 011 101 111

9. More gates NAND NOR XOR – A XOR B = [A Λ (¬B)] V [(¬A) Λ B] 9 ABOut 000 011 101 110

10. How about a two-to-one computer 10 Binary “states” for input and output: HIGH or LOW (1 or 0) 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; A Out 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 11

12. CMOS gates implementation NOT AND OR 12

13. CMOS gates: NAND 13 Gnd

14. CMOS gates: NOR 14 Vdd Gnd A B Out

15. Lab: NAND gate 15

16. Adder 16 AB Sum Carry-out 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 ABSumCarry-out 2570 9981 …………

17. The simplest adder 17 AB Sum Carry-out 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 ABSumCarry-out 0110 1101 1010 0000 Truth table

18. The simplest adder (Contd.) 18 AB Sum Carry-out 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 ABSumCarry-out 0110 1101 1010 0000 Truth table Sum= A XOR B Carry-out = A AND B

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

20. AND 20

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)] 21

22. XOR (Contd.) 22 Out

23. XOR (Contd.) 23 Out Vdd

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 24 George Boole 1815-1864

25. Integrated Circuit 25 Shared Nobel Prize in Physics 2000

26. Photolithography

28. 1969

29. 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

30. “Programmable” integrated circuit 30 AB Sum Carry-out

31. “Programmable” integrated circuit 31 AB Output Control

32. “Programmable” integrated circuit 32 AB Output Control Storage

33. “Programmable” integrated circuit 33 AB Output Control Storage

34. “Programmable” integrated circuit 34 AB Output Control Storage 0110100010101 Instruction in machine code

35. “Programmable” integrated circuit 35 AB Output Control Storage Default start instruction

36. 36 Computing vs. human performance Sources: intel.com and factmonster.com

37. 37 Computing vs. humanity Source: Intel.com and dol.gov

38. 38 http://ftp.arl.army.mil/ftp/historic-computers/png/eniac4.png Computing: 60 years ago Wiring ENIAC with a new program