Hes alive Really alive

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Hes alive! Really alive!
http//www.imdb.com/title//

• Steve Guttenberg in Short Circuit (1986)

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Computer Science 101Lecture 6
www.engraveit.co.za/.../ overview/PC20radio.jpg

• Spring Semester 2008
• Wednesday, January 23
• Week 3/18
• Albert H. Carlson

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Announcements

• HW 1 is due on Friday, January 25

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Bigger than a PC, Smaller than a Room

• Workstations
• More powerful than PCs, also more expensive
• Servers
• Used by people connecting to a network
• High Power, fairly expensive
• Client/Server actions
• Minicomputers
• Handle small businesses and hundreds to thousands
  of users
• Typically handle dumb terminals
• Losing popularity

http//www.kambach.net/images/server/s_pic3.jpg
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The Big Computers

• Mainframe
• Special purpose
• Handle large jobs
• VERY expensive
• Supercomputers
• Ultrafast up to 12 Trillion operations (flops)
  per second
• EXTREMELY expensive (government level) up to
  20MM
• Really big some as big as 5 tennis courts

de.shuttle.com/promo/ xpc_kit/supercomputer.jpg
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And where are they made?

• Making computers requires special resources
• These resources are only available in some places
• And where are the areas where computers and parts
  of computers are made?

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Significant Chip and Hardware Centers in the US
Silicon Valley
Silicon Desert
Seattle
Silicon Prairie
Minneapolis
Salt Lake City
Philadelphia
Denver
Boston
Austin
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The Parts of a Computer
Central Processing Unit (CPU)
Output
Input
Memory or Storage
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The CPU
ALU
Output Contr.
Input Contr.
RAM
ROM
Network Card
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Going Deeper

• Now that we know the basic parts, lets go deeper.
• We are going about as deep as we can before going
  to the molecular level
• We are going to the level of electronics

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Logic Functions

• There are also hardware units, called gates, that
  work with numbers called logic levels
• Binary has two logic levels 1 and 0
• 1 is represented by high levels of from 1.1V
  and 5V
• 0 is represented by low levels of 0V
• Gates do the math functions based on the inputs
  we give it. They do it automatically

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Gate/Math Functions

• AND
• OR
• NOT
• XOR

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OK, Why the Fuss?

• This is how we turn the numbers into those
  transition functions I was talking about earlier
• Lets see how we actually use the math to make
  things work. We will start with part of the ALU
  the adder (Cant do math without it!)

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The Adder

• What we want is something to do the addition of
  two SMALL, SINGLE Digit (1 bit) Numbers
• We start by noting that the rules about binary
  addition tell us ALL
• Why are we using binary?
• The answer is that it is easy in ELECTRONICS to
  use 2 values, hi and low

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Adder, continued

• The basic math functions are
• 0 0 0
• 0 1 1 0 1
• 1 1 102
• 1 1 1 112
• We restate this a bit
• 0 0 0, AND Note that 1 1 0
• 0 1 1 0 1

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Adder, continued

• What does this look like?
• A the XOR function we looked at earlier
• This means that we can use the XOR gate to make
  the resulting answer for the bit
• But, this ignores an important part of addition
  the carry we need

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The Adder, Again

• We have to generate a carry IF we have the 1 1
  option
• We really need to generate a carry if both are 1.
  What function does that remind us of?
• The AND, where 1 AND 1 1

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Still Making an Adder

• This is great, IF we only are adding one digit,
  BUT .
• What if we want to make this a building block for
  a FULL ADDER
• When we do addition, we also have to look at what
  we call the carry in. That is, what if we have
  a carry from the column before the one we are
  working in?

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Adding to the Adder

• This means that we have to deal with 3 numbers,
  A, B, and Cin
• What we end up with is an XOR circuit that takes
  3 inputs

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Adder Basics

• How do we prove this is the right answer?
• We try all combinations
• What happens when we are at the least significant
  digit?
• A We ALWAYS have NO carry in, so . We set the
  initial carry in to 0

www.soarmn.com/stanton/ photos/blackboard.jpg
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Still doing the Adder

• This ALSO affects the Carry (we will call this
  the Carry Out, or Cout)
• We can get a carry if
• A and B are both 1, or
• A and Cin are both 1, or
• B and Cin are both 1
• Changing the Cout generator takes care of this
  problem

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The Carry out
The Cout is formed by finding when one of the
conditions we specified is true. It results in
the following circuit
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Abstracting the Adder

• It is hard to draw the gates over and over again.
  Too much detail
• So, instead we draw a BOX diagram that REPRESENTS
  the circuit. It looks like

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Constructing the Adder

• Now we can construct an adder for as LARGE a
  number as we want, using these blocks
• Blocks connect together repeatedly to make up the
  final circuit
• What we now have is a way in electronics to do
  math. Isnt that what we need for the heart of
  the ALU and Computer

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The Final Adder
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The ALU

• Now, lets add the interesting logic functions
• AND
• OR
• NOT
• XOR
• We also add a way to select the output and do all
  of the math in parallel giving us what we need
  at the output

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The ALU

• Now we can do ALL of the Math and Logic, on
  demand. All electronically

www.cs.nyu.edu/.../ V22.0436-001/alu-symbol.png
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Not All People Like Hardware
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But, Logic isnt All

• Logic just makes it possible to do math
• Because of abstraction, we can use math to do all
  sorts of things
• This is the basis of what we do with a computer

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Differences in Numbers

• Cant line up numbers in columns
• What happens when we need to express the concept
  of nothing?
• Arabs invent the concept of 0
• The concept of placeholders and lining up by
  columns indicating powers
• What does a number really mean?

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An Example
5 1 5
1 0 0 0
4 10 40
8 100 800
1 0
7 1000 7000
7845
7845
1 0 0
1
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What We Just Did

• Note the following
• 1 100
• 10 101
• 100 102
• 1000 103
• etc. That is to say, if we start out from the
  right side, we can go over each column to the
  left and give the weighting of 10n-1, where n
  is the number of columns from the right

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Questions?