COMP541 160 Digital Logic and Computer Design

1. 1 COMP541 (160) Digital Logic and Computer Design Montek Singh Jan 11, 2007

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3. 3 What�s Course About? Digital logic, focusing on the design of computers Stay above transistor level Only one class on transistors and VLSI Each person designs a MIPS CPU and peripheral logic (VGA, joystick) Project like an Atari 2600 game High-level language Modern design practices

4. 4 How Can We Do This? Field Programmable Gate Arrays Chips with a lot of circuits Tens of thousands to millions of transistors Programmable We write �programs� describing design Tools translate to gates/wires Download pattern to chip

5. 5 We Will Use This Board

6. 6 Schematic Diagram

7. 7 Verilog /* * A 32-bit counter with only 4 bits of output. The idea is * to select which of the counter stages you want to pass on. * * Anselmo Lastra, November 2002 */ module cntr_32c(clk,res,out); input clk; input res; output [3:0] out; reg [31:0] count; always @ (posedge res or posedge clk) if(res) count <= 0; else count <= count + 1; assign out[3] = count[28]; assign out[2] = count[27]; assign out[1] = count[26]; assign out[0] = count[25]; endmodule

8. 8 Xilinx Software Use design tools from chip maker Have full version on lab PCs Can install on your PC ModelSim simulator or built-in

9. 9 Class Web Pages Linked from my home pagehttp://www.cs.unc.edu/~montek All notes posted Will try to put them there before class Lab documents there also See Blackboard for grades

10. 10 Textbook and Syllabus Largely follow Prof. Lastra�s syllabus Morris Mano and Charles Kime Logic and Logic and Computer Design Fundamentals, 3rd Edition Prentice Hall, 2004 Will largely follow text Slightly different order More emphasis on HLL

11. 11 Overview of Textbook Chapters 1-6: Digital logic Combinational and sequential Chapter 7-8: Register Transfer and State Machines Chapter 9: Memories Chapters 10-12: Computer design Chapter 13: I/O Chapter 14: Memory Hierarchies

12. 12 Order of Topics Will change order from that in book To try to get you working on interesting labs sooner Move sequential design earlier Then backfill details on combinational design

13. 13 May Also Need COMP120 book For MIPS reference How many have one? I can copy the few necessary pages Verilog reference Book optional Web pages � see course home page

14. 14 Grading Labs � 35% Easier at first; later ones will count more Homework � 20% Two tests spaced evenly � 12.5% each Final � 20% (optional for some)

15. 15 Labs Paced slowly at first Familiarization with tools, simple combinational design, design a digital lock or similar Peripheral � VGA, opt. keyboard interface or joystick Build up computer components Registers, ALU, decoder Assemble a simple MIPS Add more features, enough for simple computer Final demo � game or similar

16. 16 Lab Sections No lab this Friday You need a little more info to begin Begin next week Lab is in SN 027, down the hall by the back entrance

17. 17 Late Policy Homework assignments and lab reports due by class time Labs due on Tuesday after the lab period One class late, 10 points off Two classes late, 25 points off Not accepted later

18. 18 What�s Your Background? Course experience Work, etc. Which COMP120? What�s your intent in taking class? Questions?

19. 19 Office Hours Would like to wait a week to set Send email if you want to meet

20. 20 Now Shift to Technology Should be review for all of you

21. 21 Digital vs. Analog Analog � infinite resolution Like (old fashioned) radio dial We�ll do very little with analog VGA, maybe sound Digital � a finite set of values Like money Can�t get smaller than cents Typically also has maximum value

22. 22 Binary Signaling Zero volts FALSE or 0 3.3 or 5 volts TRUE or 1 Modern chips down to 1V Why not multilevel signaling?

23. 23 Discrete Data Some data inherently discrete Names (sets of letters) Some quantized Music recorded from microphone Note that other examples like music from CD or electronic keyboard already quantized Mouse movement is quantized Well, some mice

24. 24 Numbers and Arithmetic I�ve put most of these slides at end Backup in case you�ve forgotten Review of binary numbers, Hexadecimal,Arithmetic Let�s cover Other codes, parity

25. 25 BCD Binary Coded Decimal Decimal digits stored in binary Four bits/digit Like hex, except stops at 9 Example 931 is coded as 1001 0011 0001 Remember: these are just encodings. Meanings are assigned by us.

26. 26 Other Codes Exist Non positional Example: Gray Code Only one bit changes at a time 000,001,011,010,110,111,101,100 Why is this useful? Actually there�s a family of Gray codes

27. 27 Shaft Encoder

28. 28 Character Codes From numbers to letters ASCII Stands for American Standard Code for Information Interchange Only 7 bits defined Unicode You may make up your own code for the MIPS VGA

29. 29 ASCII table

30. 30 Even Parity Sometimes high-order bit of ASCII coded to enable detection of errors Even parity � set bit to make number of 1�s even Examples A (01000001) with even parity is 01000001 C (01000011) with even parity is 11000011

31. 31 Odd Parity Similar except make the number of 1�s odd Examples A (01000001) with odd parity is 11000001 C (01000011) with odd parity is 01000011

32. 32 Error Detection Note that parity detects only simple errors One, three, etc. bits More complex methods exist Some that enable recovery of original info Cost is more redundant bits

33. 33 Today�s Topics Introduction Digital logic Number systems Arithmetic Codes Parity The encoding is key Standards are used to agree on encodings Special purpose codes for particular uses

34. 34 Homework None, but� I expect you to know number systems well and be able to do conversions and arithmetic Decimal � Binary Binary � Decimal Decimal � Hex Hex � Decimal Can do some of the problems � 1-2, 1-4, 1-7 if you think you need a refresher. Answers on book website.

35. 35 Reading Skim chapter 1 Quick read to make sure you�re comfortable with material Read Chapter 2

36. 36 Next Week Combinational Logic Basics Lab preview I�ll demo tools in class, probably Thursday Lab on Friday the 19th Schematic capture Maybe simple Verilog Run on FPGA

37. 37 Lab Walkthrough Let�s go see the lab Shared with LEGO 1st year seminar

38. 38 Backup Slides Should be all review material

39. 39 Binary Numbers Strings of binary digits (�bits�) One bit can store a number from 0 to 1 n bits can store numbers from 0 to 2n http://fls.cll.wayne.edu/olmt/BINARY/ is a nice web page on Binary. http://fls.cll.wayne.edu/olmt/BINARY/ is a nice web page on Binary.

40. 40 Binary � Powers of 2 Positional representation Each digit represents a power of 2 So 101 binary is 1 � 22 + 0 � 21 + 1 � 20 or 1 � 4 + 0 � 2 + 1 � 1 = 5

41. 41 Converting Binary to Decimal Easy, just multiply digit by power of 2 Just like a decimal number is represented Example follows

42. 42 Binary ? Decimal Example

43. 43 Decimal to Binary A little more work than binary to decimal Some examples 3 = 2 + 1 = 11 (that�s 1�21 + 1�20) 5 = 4 + 1 = 101 (that�s 1�22 + 0�21 + 1�20)

44. 44 Algorithm � Decimal to Binary Find largest power-of-two smaller than decimal number Make the appropriate binary digit a �1� Subtract the power of 2 from decimal Do the same thing again

45. 45 Decimal ? Binary Example Convert 28 decimal to binary

46. 46 Hexadecimal Strings of 0s and 1s too hard to write Use base-16 or hexadecimal � 4 bits

47. 47 Hexadecimal Letters to represent 10-15

48. 48 Hex to Binary Convention � write 0x before number Hex to Binary � just convert digits

49. 49 Binary to Hex Just convert groups of 4 bits

50. 50 Hex to Decimal Just multiply each hex digit by decimal value, and add the results.

51. 51 Decimal to Hex Analogous to decimal ? binary. Find largest power-of-16 smaller than decimal number Divide by power-of-16. The integer result is hex digit. The remainder is new decimal number. Do the same thing again

52. 52 Decimal to Hex

53. 53 Octal Octal is base 8 Similar to hexadecimal Conversions Less convenient for use with 8-bit bytes

54. 54 Arithmetic -- addition Binary similar to decimal arithmetic

55. 55 Arithmetic -- subtraction

56. 56 Arithmetic -- multiplication

57. 57 Hexadecimal Arithmetic Similar If you�re doing by hand, easiest to convert each set of digits to decimal and back Skill is not very useful�