COMP541 Digital Logic and Computer Design

1
COMP541 Digital Logic and Computer Design

• Montek Singh
• Jan 9, 2012

2
Todays Topics

• Course description
• Whats it about
• Mechanics grading, etc.
• Material from Chapter 1 (self-study review)
• What is digital logic?
• Binary signaling
• Number systems
• Codes

3
Whats 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

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Focus

• Stay above transistor level
• At most one class on transistors and VLSI
• Expect you to know assembly language programming

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More Than Just Architecture

• Designing and implementing a computer is also
  about
• Managing complexity (hierarchy, modularity,
  regularity).
• Debugging
• Testing and verifying

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The Three -Ys

• Hierarchy
• A system divided into modules and submodules
• Modularity
• Having well-defined functions and interfaces
• Regularity
• Encouraging uniformity, so modules can be easily
  reused

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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

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We Will Use This Board
Whats on it?
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Schematic Diagram

• Old fashioned way to describe logic
• Still useful for documentation

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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 30 out
• reg 310 count
• always _at_ (posedge res or posedge clk)
• if(res)
• count lt 0
• else
• count lt count 1

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Xilinx Software

• Use design tools from chip maker
• Have full version on lab PCs
• Can install on your PC
• Download from web

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Class Web Pages

• Will be up by Thursdays class
• Linked from my home pagehttp//www.cs.unc.edu/mo
  ntek
• 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

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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?ISBN9
  780123704979

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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.

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Order of Topics

• Will change order from that in book
• To try to get you working on interesting labs
  sooner

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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

17
Grading

• Labs 35
• Easier at first later ones will count more
• Lab final project 15
• Homework 25
• Two tests spaced evenly 12.5 each

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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

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Lab Sections

• No lab this Friday
• You need a little more info to begin
• Begin next week
• Lab is in FB007

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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

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Whats Your Background?

• Course experience
• Work, etc.
• Which COMP411?
• Whats your intent in taking class?
• Questions?

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Office Hours

• Would like to wait a week to set
• Send email if you want to meet in the mean time

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Now Shift to Technology

• Should be review for all of you

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Digital vs. Analog

• Analog infinite resolution
• Like (old fashioned) radio dial
• Well do very little with analog
• VGA, maybe sound
• Digital a finite set of values
• Like money
• Cant get smaller than cents
• Typically also has maximum value

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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?

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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

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Numbers and Arithmetic

• I have put most of these slides at end
• Backup in case youve forgotten
• Review of binary numbers, Hexadecimal,Arithmetic
  
• Lets cover
• Other codes, parity

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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.

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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 theres a family of Gray codes

Ref http//lib-www.lanl.gov/numerical/bookcpdf/c2
0-2.pdf
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Shaft Encoder
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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

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ASCII table
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Even Parity

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

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Odd Parity

• Similar except make the number of 1s odd
• Examples
• A (01000001) with odd parity is 11000001
• C (01000011) with odd parity is 01000011

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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

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Todays 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

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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.

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Reading

• Read Chapter 1

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Next Class

• Combinational Logic Basics
• Next Week Lab preview
• I will demo tools in class, probably Wednesday

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Backup Slides

• Should be all review material

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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

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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

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Converting Binary to Decimal

• Easy, just multiply digit by power of 2
• Just like a decimal number is represented
• Example follows

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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
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Decimal to Binary

• A little more work than binary to decimal
• Some examples
• 3 2 1 11 (thats 121 120)
• 5 4 1 101 (thats 122 021 120)

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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

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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
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Hexadecimal

• Strings of 0s and 1s too hard to write
• Use base-16 or hexadecimal 4 bits

Dec Bin Hex
0 0000 0
1 0001 1
2 0010 2
3 0011 3
4 0100 4
5 0101 5
6 0110 6
7 0111 7
Dec Bin Hex
8 1000 8
9 1001 9
10 1010 ?
11 1011 ?
12 1100 ?
13 1101 ?
14 1110 ?
15 1111 ?
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Hexadecimal

• Letters to represent 10-15

Dec Bin Hex
0 0000 0
1 0001 1
2 0010 2
3 0011 3
4 0100 4
5 0101 5
6 0110 6
7 0111 7
Dec Bin Hex
8 1000 8
9 1001 9
10 1010 a
11 1011 b
12 1100 c
13 1101 d
14 1110 e
15 1111 f

• Power of 2

• Size of byte

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Hex to Binary
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

• Convention write 0x before number
• Hex to Binary just convert digits

0x2ac
0x2ac 001010101100
No magic remember hex digit 4 bits
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Binary to Hex
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

• Just convert groups of 4 bits

101001101111011
1011
0101 ?
0111 ?
0011 ?
101001101111011 0x537b
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Hex to Decimal
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
14 e
15 f

• Just multiply each hex digit by decimal value,
  and add the results.

0x2ac
2 256
10 16
12 1
684
???? ???? ???? ????
163 162 161 160
4096 256 16 1
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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

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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
14 e
15 f
684
0x2__
684/256 2
684256 172
0x2a_
172/16 10 a
0x2ac
17216 12 c
???? ???? ???? ????
163 162 161 160
4096 256 16 1
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Octal

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

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Arithmetic -- addition

• Binary similar to decimal arithmetic

1 0 1 1 0 0
1 0 1 1 0
1 0 1 1 1
No carries
Carries
0 1 1 0 0
1 0 0 0 1
1 0 1 1 0 1
1 1 1 0 1
11 is 2 (or 102), which results in a carry
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Arithmetic -- subtraction
0 0 1 1 0
1 1 1 1 0
- 1 0 0 1 1
No borrows
Borrows
1 0 1 1 0
- 1 0 0 1 0
0 1 0 1 1
0 0 1 0 0
0 - 1 results in a borrow
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Arithmetic -- multiplication
Successive additions of multiplicand or
zero, multiplied by 2 (102). Note that
multiplication by 102 just shifts bits left.
1 0 1 1
X 1 0 1
1 0 1 1
0 0 0 0
1 0 1 1
1 1 0 1 1 1