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

2. 2 Today’s Topics  Course description What’s it about What’s it about Mechanics: grading, etc. Mechanics: grading, etc.  Material from Chapter 1 (review) What is digital logic? What is digital logic? Binary signaling Binary signaling Number systems Number systems Codes Codes

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 Only one class on transistors and VLSI  Each person designs a MIPS CPU and peripheral logic (VGA, joystick) and peripheral logic (VGA, joystick) Project like an Atari 2600 game Project like an Atari 2600 game  High-level language Modern design practices Modern design practices

4. 4 How Can We Do This?  Field Programmable Gate Arrays Chips with a lot of circuits Chips with a lot of circuits  Tens of thousands to millions of transistors Programmable 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. 7Verilog/* * A 32-bit counter with only 4 bits of output. The idea is * 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. * to select which of the counter stages you want to pass on. * * Anselmo Lastra, November 2002 * Anselmo Lastra, November 2002 */ */ module cntr_32c(clk,res,out); module cntr_32c(clk,res,out); input clk; input clk; input res; input res; output [3:0] out; output [3:0] out; reg [31:0] count; reg [31:0] count; always @ (posedge res or posedge clk) if(res) if(res) count <= 0; else count <= count + 1; count <= count + 1; assign out[3] = count[28]; assign out[3] = count[28]; assign out[2] = count[27]; assign out[2] = count[27]; assign out[1] = count[26]; assign out[1] = count[26]; assign out[0] = count[25]; 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 page http://www.cs.unc.edu/~montek http://www.cs.unc.edu/~montek  All notes posted Will try to put them there before class 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 Slightly different order More emphasis on HLL More emphasis on HLL

11. 11 Overview of Textbook  Chapters 1-6: Digital logic Combinational and sequential 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 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 For MIPS reference How many have one? How many have one? I can copy the few necessary pages I can copy the few necessary pages  Verilog reference Book optional Book optional Web pages – see course home page Web pages – see course home page

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

15. 15Labs  Paced slowly at first Familiarization with tools, simple combinational design, design a digital lock or similar 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 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 You need a little more info to begin Begin next week 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 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 Like (old fashioned) radio dial We’ll do very little with analog We’ll do very little with analog  VGA, maybe sound  Digital – a finite set of values Like money Like money Can’t get smaller than cents Can’t get smaller than cents Typically also has maximum value Typically also has maximum value

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

23. 23 Discrete Data  Some data inherently discrete Names (sets of letters) Names (sets of letters)  Some quantized Music recorded from microphone Music recorded from microphone Note that other examples like music from CD or electronic keyboard already quantized Note that other examples like music from CD or electronic keyboard already quantized Mouse movement is 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 Backup in case you’ve forgotten  Review of binary numbers, Hexadecimal, Arithmetic  Let’s cover Other codes, parity Other codes, parity

25. 25BCD  Binary Coded Decimal  Decimal digits stored in binary Four bits/digit Four bits/digit Like hex, except stops at 9 Like hex, except stops at 9 Example Example 931 is coded as 1001 0011 0001 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 Only one bit changes at a time 000,001,011,010,110,111,101,100 000,001,011,010,110,111,101,100 Why is this useful? Why is this useful? Actually there’s a family of Gray codes Actually there’s a family of Gray codes Ref: http://lib-www.lanl.gov/numerical/bookcpdf/c20-2.pdf

27. 27 Shaft Encoder

28. 28 Character Codes  From numbers to letters  ASCII Stands for American Standard Code for Information Interchange Stands for American Standard Code for Information Interchange Only 7 bits defined 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 One, three, etc. bits  More complex methods exist  Some that enable recovery of original info Cost is more redundant bits 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 Standards are used to agree on encodings Special purpose codes for particular uses Special purpose codes for particular uses

34. 34Homework  None, but…  I expect you to know number systems well and be able to do conversions and arithmetic Decimal – Binary Decimal – Binary Binary – Decimal Binary – Decimal Decimal – Hex Decimal – Hex Hex – Decimal 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. 35Reading  Skim chapter 1 Quick read to make sure you’re comfortable with material 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 I’ll demo tools in class, probably Thursday  Lab on Friday the 19 th Schematic capture Schematic capture Maybe simple Verilog Maybe simple Verilog Run on FPGA Run on FPGA

37. 37 Lab Walkthrough  Let’s go see the lab  Shared with LEGO 1 st 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 One bit can store a number from 0 to 1 n bits can store numbers from 0 to 2 n n bits can store numbers from 0 to 2 n

40. 40 Binary – Powers of 2  Positional representation  Each digit represents a power of 2 So 101 binary is 1 2 2 + 0 2 1 + 1 2 0 1 2 2 + 0 2 1 + 1 2 0or 1 4 + 0 2 + 1 1 = 5 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 76543210 27272727 26262626 25252525 24242424 23232323 22222222 21212121 20202020 1286432168421 10011100 128 + 0 + 0 + 16 + 8 + 4 + 0 + 0 = 156 What is 10011100 in decimal?

43. 43 Decimal to Binary  A little more work than binary to decimal  Some examples 3 = 2 + 1 = 11 (that’s 12 1 + 12 0 ) 3 = 2 + 1 = 11 (that’s 12 1 + 12 0 ) 5 = 4 + 1 = 101 (that’s 12 2 + 02 1 + 12 0 ) 5 = 4 + 1 = 101 (that’s 12 2 + 02 1 + 12 0 )

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 76543210 27272727 26262626 25252525 24242424 23232323 22222222 21212121 20202020 1286432168421 32 is too large, so use 16 Binary  10000Decimal  28 – 16 = 12 Binary  11000Decimal  12 – 8 = 4 Next is 8 Binary  11100Decimal  4 – 4 = 0 Next is 4

46. 46Hexadecimal  Strings of 0s and 1s too hard to write  Use base-16 or hexadecimal – 4 bits DecBinHex 000000 100011 200102 300113 401004 501015 601106 701117DecBinHex810008 910019 101010? 111011? 121100? 131101? 141110? 151111?

47. 47Hexadecimal  Letters to represent 10-15 DecBinHex 000000 100011 200102 300113 401004 501015 601106 701117DecBinHex810008 910019 101010a 111011b 121100c 131101d 141110e 151111f Power of 2Power of 2 Size of byteSize of byte Why use base 16?

48. 48 Hex to Binary  Convention – write 0x before number  Hex to Binary – just convert digits BinHex 00000 00011 00102 00113 01004 01015 01106 01117 10008 10019 1010a 1011b 1100c 1101d 1110e 1111f 0x2ac 001010101100 0x2ac = 001010101100 No magic – remember hex digit = 4 bits

49. 49 Binary to Hex  Just convert groups of 4 bits BinHex 00000 00011 00102 00113 01004 01015 01106 01117 10008 10019 1010a 1011b 1100c 1101d 1110e 1111f 101001101111011 1011 537b 101001101111011 = 0x537b 0101  0111  0011 

50. 50 Hex to Decimal  Just multiply each hex digit by decimal value, and add the results.  16 3 16 2 16 1 16 0 4096256161 0x2ac 2 256 + 10 16 + 12 1 = 684 DecHex00 11 22 33 44 55 66 77 88 99 10a 11b 12c 13d 14e 15f

51. 51 Decimal to Hex Analogous to decimal  binary. 1. Find largest power-of-16 smaller than decimal number 2. Divide by power-of-16. The integer result is hex digit. 3. The remainder is new decimal number. 4. Do the same thing again

52. 52 Decimal to Hex  16 3 16 2 16 1 16 0 4096256161 DecHex00 11 22 33 44 55 66 77 88 99 10a 11b 12c 13d 14e 15f 684 684/256 = 2 0x2__ 684%256 = 172 172/16 = 10 = a 0x2a_ 172%16 = 12 = c 0x2ac

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

54. 54 Arithmetic -- addition  Binary similar to decimal arithmetic 01100 +10001 11101 No carries10110010110 +10111 101101 Carries 1+1 is 2 (or 10 2 ), which results in a carry

55. 55 Arithmetic -- subtraction 10110 -10010 00100 No borrows0011011110 -10011 01011 Borrows 0 - 1 results in a borrow

56. 56 Arithmetic -- multiplication 1011 0000 1011 110111 Successive additions of multiplicand or zero, multiplied by 2 (10 2 ). Note that multiplication by 10 2 just shifts bits left. 1011X 101

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…