1 COMP541 (160) Digital Logic and Computer Design Montek Singh Jan 11, 2007
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 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 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 We Will Use This Board
6 Schematic Diagram
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; (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 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 Class Web Pages Linked from my home page 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 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 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 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 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
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)
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 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 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 What’s Your Background? Course experience Work, etc. Which COMP120? What’s your intent in taking class? Questions?
19 Office Hours Would like to wait a week to set Send if you want to meet
20 Now Shift to Technology Should be review for all of you
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 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 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 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
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 is coded as Remember: these are just encodings. Meanings are assigned by us.
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, ,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:
27 Shaft Encoder
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 ASCII table
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 ( ) with even parity is C ( ) with even parity is
31 Odd Parity Similar except make the number of 1’s odd Examples A ( ) with odd parity is C ( ) with odd parity is
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 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
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.
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 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 Lab Walkthrough Let’s go see the lab Shared with LEGO 1 st year seminar
38 Backup Slides Should be all review material
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 Binary – Powers of 2 Positional representation Each digit represents a power of 2 So 101 binary is or = = 5
41 Converting Binary to Decimal Easy, just multiply digit by power of 2 Just like a decimal number is represented Example follows
42 Binary Decimal Example = 156 What is in decimal?
43 Decimal to Binary A little more work than binary to decimal Some examples 3 = = 11 (that’s ) 3 = = 11 (that’s ) 5 = = 101 (that’s ) 5 = = 101 (that’s )
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 Decimal Binary Example Convert 28 decimal to binary 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
46Hexadecimal Strings of 0s and 1s too hard to write Use base-16 or hexadecimal – 4 bits DecBinHex DecBinHex ? ? ? ? ? ?
47Hexadecimal Letters to represent DecBinHex DecBinHex a b c d e f Power of 2Power of 2 Size of byteSize of byte Why use base 16?
48 Hex to Binary Convention – write 0x before number Hex to Binary – just convert digits BinHex a 1011b 1100c 1101d 1110e 1111f 0x2ac x2ac = No magic – remember hex digit = 4 bits
49 Binary to Hex Just convert groups of 4 bits BinHex a 1011b 1100c 1101d 1110e 1111f b = 0x537b 0101 0111 0011
50 Hex to Decimal Just multiply each hex digit by decimal value, and add the results. x2ac = 684 DecHex a 11b 12c 13d 14e 15f
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 Decimal to Hex DecHex a 11b 12c 13d 14e 15f /256 = 2 0x2__ 684%256 = /16 = 10 = a 0x2a_ 172%16 = 12 = c 0x2ac
53Octal Octal is base 8 Similar to hexadecimal Conversions Conversions Less convenient for use with 8-bit bytes
54 Arithmetic -- addition Binary similar to decimal arithmetic No carries Carries 1+1 is 2 (or 10 2 ), which results in a carry
55 Arithmetic -- subtraction No borrows Borrows results in a borrow
56 Arithmetic -- multiplication Successive additions of multiplicand or zero, multiplied by 2 (10 2 ). Note that multiplication by 10 2 just shifts bits left. 1011X 101
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…