Transcript Lecture 1

COMP541
Digital Logic and
Computer Design
Montek Singh
Jan 9, 2012
1
Today’s Topics
 Course description
 What’s it about
 Mechanics: grading, etc.
 Material from Chapter 1 (self-study review)
 What is digital logic?
 Binary signaling
 Number systems
 Codes
2
What’s Course About?
 Digital
logic, focusing on the design of computers
 Stay mostly at a high level (i.e., above transistors)
 Each person designs a MIPS CPU
 and peripheral logic (VGA, joystick)
 Project like an Atari 2600 game
 High-level language
 Modern design practices
3
Focus
 Stay above transistor
level
 At most one class on
transistors and VLSI
assembly language
programming
focus of this course
 Expect you to know
Application
Software
programs
Operating
Systems
device drivers
Architecture
instructions
registers
Microarchitecture
datapaths
controllers
Logic
adders
memories
Digital
Circuits
AND gates
NOT gates
Analog
Circuits
amplifiers
filters
Devices
transistors
diodes
Physics
electrons
4
More Than Just Architecture
 Designing and implementing a computer is also
about
 Managing complexity (hierarchy, modularity, regularity).
 Debugging
 Testing and verifying
5
The Three -Y’s
 Hierarchy
 A system divided into modules and submodules
 Modularity
 Having well-defined functions and interfaces
 Regularity
 Encouraging uniformity, so modules can be easily reused
How Can We Do This?
 Labs on Fridays
 Use: Field Programmable Gate Arrays (FPGAs)
 Chips with a lot of circuits
 Tens of thousands to millions of transistors
 Programmable
 We write descriptions of the design
 “programs” describing design
 Tools translate to gates/wires
 Download pattern/interconnection to chip
 Sort of like burning music to a rewritable CD
7
We Will Use This Board
What’s on it?
8
Schematic Diagram
• Old fashioned way to describe logic
• Still useful for documentation
9
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
10
Xilinx Software
 Use design tools from chip maker
 Have full version on lab PCs
 Can install on your PC
 Download from web
11
Class Web Pages
 Will be up by Thursday’s class
 Linked from my home page
http://www.cs.unc.edu/~montek
 All lecture slides posted there
 Will try to put them there before class
 Schedule, homework, etc. posted there
 Lab documents there also
 See Blackboard/Sakai for scores/grades
12
Textbook
 Harris and Harris
 Digital Design and Computer Architecture
 Morgan Kaufmann, 2007
 Amazon has for $70
 Extra material on
http://www.elsevierdirect.com/companion.jsp?ISBN=9780123704979
13
Overview of Textbook
 Chapters 1-5: Digital logic
 Combinational, sequential, basic circuits, HDL
 Chapter 6: Architecture
 Fast – review for those who took COMP 411
 Chapter 7: Microarchitectures
 Chapters 8: Memories
 Appendix A: Implementation
 FPGAs, etc.
14
Order of Topics
 Will change order from that in book
 To try to get you working on interesting labs sooner
15
May Also Need
 COMP411 textbook (Patterson/Hennessy)
 For MIPS reference
 How many have one?
 I can copy the few necessary pages
 Verilog reference
 Book optional
 Web pages – see course home page
16
Grading
 Labs – 35%
 Easier at first; later ones will count more
 Lab final project – 15%
 Homework – 25%
 Two tests spaced evenly – 12.5% each
17
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
18
Lab Sections
 No lab this Friday
 You need a little more info to begin
 Begin next week
 Lab is in FB007
19
Late Policy
 Homework assignments and lab reports due by class
 Labs due on Monday after the lab period
 One class late, 10 points off
 Two classes late, 25 points off
 Not accepted later
20
What’s Your Background?
 Course experience
 Work, etc.
 Which COMP411?
 What’s your intent in taking class?
 Questions?
21
Office Hours
 Would like to wait a week to set
 Send email if you want to meet in the mean time
22
Now Shift to Technology
Should be review for all of you
23
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
24
Binary Signaling
 Zero volts
 FALSE or 0
 5 or 3.3 (or 1.8 or 1.5) volts
 TRUE or 1
 Modern chips down to 1V
 Why not multilevel signaling?
25
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
26
Numbers and Arithmetic
 I have 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
27
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
by us.
encodings. Meanings are assigned
28
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
Ref: http://lib-www.lanl.gov/numerical/bookcpdf/c20-2.pdf
29
Shaft Encoder
30
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
31
ASCII table
32
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
33
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
34
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
35
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
36
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 – 1.7 to 1.27 are all about
conversion – if you think you need a refresher. Answers to
odd numbered on book website.
37
Reading
 Read Chapter 1
38
Next Class
 Combinational Logic Basics
Next Week: Lab preview
 I will demo tools in class, probably Wednesday
39
Backup Slides
Should be all review material
40
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
41
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
42
Converting Binary to Decimal
 Easy, just multiply digit by power of 2
 Just like a decimal number is represented
 Example follows
43
Binary  Decimal Example
7
6
5
4
3
2
1
0
27
26
25
24
23
22
21
20
128
64
32
16
8
4
2
1
What is 10011100 in decimal?
1
0
0
1
1
1
0
0
128 + 0 + 0 + 16 + 8 + 4 + 0 + 0 = 156
44
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)
45
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
46
Decimal  Binary Example
 Convert 28 decimal to binary
32 is too large, so use 16
Binary  10000
Decimal  28 – 16 = 12
Next is 8
Binary  11000
Decimal  12 – 8 = 4
Next is 4
Binary  11100
Decimal  4 – 4 = 0
7
6
5
4
3
2
1
0
27
26
25
24
23
22
21
20
128
64
32
16
8
4
2
1
47
Hexadecimal
 Strings of 0s and 1s too hard to write
 Use base-16 or hexadecimal – 4 bits
Dec
Bin
Hex
Dec
Bin
Hex
0
0000
0
8
1000
8
1
0001
1
9
1001
9
2
0010
2
10
1010
?
3
0011
3
11
1011
?
4
0100
4
12
1100
?
5
0101
5
13
1101
?
6
0110
6
14
1110
?
7
0111
7
15
1111
?
48
Hexadecimal
 Letters to represent 10-15
Dec
Bin
Hex
Dec
Bin
Hex
0
0000
0
8
1000
8
1
0001
1
9
1001
9
2
0010
2
10
1010
a
3
0011
3
11
1011
b
4
0100
4
12
1100
c
5
0101
5
13
1101
d
6
0110
6
14
1110
e
•Power of 2
7
0111
7
15
1111
f
•Size of byte
Why use
base 16?
49
Hex to Binary
Bin
Hex
0000
0
0001
1
0010
2
 Convention – write 0x before number
0011
3
 Hex to Binary – just convert digits
0100
4
0101
5
0110
6
0111
7
1000
8
1001
9
1010
a
1011
b
1100
c
1101
d
1110
e
1111
f
0x2ac
0010
1010 1100
0x2ac = 001010101100
No magic – remember hex digit = 4 bits
50
Binary to Hex
 Just convert groups of 4 bits
101001101111011
0101  0011  0111  1011
5
3
7
b
101001101111011 = 0x537b
Bin
Hex
0000
0
0001
1
0010
2
0011
3
0100
4
0101
5
0110
6
0111
7
1000
8
1001
9
1010
a
1011
b
1100
c
1101
d
1110
e
1111
f
51
Hex to Decimal
Dec
Hex
0
0
 Just multiply each hex digit by decimal value,
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
a
11
b
12
c
13
d
14
e
15
f
and add the results.
0x2ac
2 • 256

+ 10 • 16 + 12 • 1 = 684



163
162
161
160
4096
256
16
1
52
Decimal to Hex
1.
2.
3.
4.
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
53
Decimal to Hex
Dec
Hex
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
a
11
b
12
c
13
d
160
14
e
1
15
f
684
0x2__
684/256 = 2
684%256 = 172
0x2a_
172%16 = 12 = c 0x2ac
172/16 = 10 = a

163
4096

162
256

161
16

54
Octal
 Octal is base 8
 Similar to hexadecimal
 Conversions
 Less convenient for use with 8-bit bytes
55
Arithmetic -- addition
 Binary similar to decimal arithmetic
1
No carries
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
+ 1
0
0
0
1
+ 1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
Carries
1+1 is 2 (or 102), which results in a carry
56
Arithmetic -- subtraction
No borrows
-
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
-
0
0
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
Borrows
0 - 1 results in a borrow
57
Arithmetic -- multiplication
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
1
X
1
Successive additions of
multiplicand or zero,
multiplied by 2 (102).
Note that multiplication
by 102 just shifts bits
left.
1
58