Computer Logic, Logic Gates, and Building Circuits

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Computer Logic, Logic Gates,and Building Circuits
Image Intel Museum
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Logic and Computers

• The technology inside of computers (and in fact
  all logical ideas) is based on several simple
  logic operations
• AND
• OR
• NOT
• These logical operations are related to real
  world equivalents

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What does AND mean?

• When we say AND, formally we mean that
  something is true only when both parts of it are
  true.
• If the stove is on AND waters in the kettle,
  then we will make steam.
• If either part isnt there, then the result wont
  be true.

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What does AND mean in Logic?

• AND takes two inputs and produces the value TRUE
  if both inputs are TRUEs.
• So, with the inputs T AND T output is T
• T AND F output is F
• F AND T output is F
• F AND F output is F
• (Just like in the real world.)

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A Truth Table

• A truth table is a convenient way to write down
  the definition of a logic operation.
• Lets use 1s for True and 0s for False
• Heres the table for AND
• input input output
• 1 1 1
• 1 0 0
• 0 1 0
• 0 0 0

Output of 1 onlywhen both inputsare 1.
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Truth Table for OR and NOT

• OR NOT
• input input output input output
• 1 1 1 1 0
• 1 0 1 0 1
• 0 1 1
• 0 0 0

This just givesthe opposite.
We only need one of the inputsto be true, but if
both are true,thats ok, too.
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A Logic Gate

• A logic gate is a small computer circuit that
  simulates one of the logic operators weve seen.
• There are one or two wires that go into the gate
  that represent the input.
• There is one output wire that represents the
  result of the logic operation.
• When the power is on, that means True.

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Logic Gates

• When drawing diagramsof logic circuits, weuse
  some traditionalshapes for each one.

A
C
NOT
If A is off, turn on C.
AND
AND
A
A
C
C
OR
B
B
If A and B are on, turn on C.
If A or B is on, turn on C.
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What have we seen so far?

• We saw what a logic gate is. We saw how to use
  one.
• Now we will see how they work inside.
• But we will return to the LogSim program later to
  see how we can combine multiple logic gates
  together to do useful work.

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But whats inside the box?

• How do we build an individual logic gate?
• Pattern on the Stone chapter 1 shows to build
  each logic gate from tinker toys, water pipes,
  or wires.
• But real computers today use logic gates built
  out of small electronic devices.

Image Tinkertoy Website
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OR Gate from Tinker Toys
spring
Pushing a pole to the right means TRUE.
moveable
Push either one of theseto make the output
polemove.
Not moveable
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Building Gates from Wires
Lighting-up means TRUE for output.
Flipping a switch means TRUE for input.

-
AND
OR

-
How many switches must you turn on in
eachcircuit in order for the light bulb to light
up?
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Real Computers

• Real computers are not built from tinker toys or
  any of the other wacky approaches shown in the
  Pattern on the Stone.
• Computers today use logic gates that are built
  out of small electronic devices called
  transistors.

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Whats a Transistor
Image Intel Museum
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Why are transistors special?

• Transistors are like real switches, but
• 1. They have no moving parts.
• 2. They can be turned on and off by an electric
  signal.
• 3. You could hook the output of one switch to the
  input of another since they both use electricity!
• So that means They are small and fast.
• In fact, as transistors get smaller and faster,
  so do computers.

ControlSignal
Image Intel Museum
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Computers Get Smaller ENIAC

• The tremendous size of the first electronic
  computer, built here at Penn, was because the
  transistors used to built it were the size of
  lightbulbs.
• Modern transistors are microscopic.
• Thats what we have laptop and handheld
  computers nowadays.

Image Van Pelt Library ENIAC Exhibit
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Sizes of Transistors

• Look at the transistors samples in class.
• Moores Law is a famous observation that
  Researchers tend to shrink transistor sizes in
  half every 18 months.

Transistors shrink so we can make chips smaller
and fit more on a single chip.
Image Intel Research
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A Transistor

• A transistor controlswhether a switch ison or
  off.
• It turns off its switch when its given an
  electric signal.
• When there is no power on the signal line, the
  transistor turns the switch on.

Transistor
signal
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A Transistor

• A transistor controlswhether a switch ison or
  off.
• It turns off its switch when its given an
  electric signal.
• When there is no power on the signal line, the
  transistor turns the switch on.

TransistorOFF
signalON
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A Transistor

• A transistor controlswhether a switch ison or
  off.
• It turns off its switch when its given an
  electric signal.
• When there is no power on the signal line, the
  transistor turns the switch on.

TransistorON
signalOFF
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Logic Gates from Transistors

• For example, we will build a NOT gate from a
  transistor.

extrapowersource
Transistor
Output fromNOT gate.
Input toNOT gate.
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Logic Gates from Transistors

• For example, we will build a NOT gate from a
  transistor.

extrapowersource
TransistorOFF
Output fromNOT gateis OFF.
Input toNOT gateis ON.
NOT 1 ? 0
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Logic Gates from Transistors

• For example, we will build a NOT gate from a
  transistor.

extrapowersource
TransistorON
Output fromNOT gateis ON.
Input toNOT gateis OFF.
NOT 0 ? 1
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Summary A Hierarchy of Parts

• We started with TRANSISTORS.
• We built some LOGIC GATES.
• Can we build useful stuff out of logic
  gates?How can we combine them?

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Building Exclusive OR

• One or the other but not both.
• Different than OR.
• _

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Building Exclusive OR

• One or the other but not both.
• Different than OR.
• Want output TRUE when eitherInput 1 is TRUE
  and Input 2 is FALSE orInput 1 is FALSE and
  Input 2 is TRUE

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Building Exclusive OR

• One or the other but not both.
• Different than OR.
• Want output TRUE when eitherInput 1 is TRUE
  and Input 2 is FALSE orInput 1 is FALSE and
  Input 2 is TRUE

Can replace False with NOT TRUE.
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Building Exclusive OR

• Want output TRUE when eitherInput 1 is TRUE and
  Input 2 is NOT TRUE orInput 1 is NOT TRUE and
  Input 2 is TRUE

AND
NOT
Input 1
OR
Output
Input 2
AND
NOT
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If theres extra time

• Can we build an AND circuit using only NOT and OR
  gates?

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If theres extra time
AND should be FALSE if either Input 1 is NOT
TRUE or Input 2 is NOT TRUE.
Input 1
NOT
Output
OR
NOT
Input 2
NOT
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Credits

• The Intel Museum
• http//www.intel.com/education/transworks/
• Intel Research Website
• http//www.intel.com/research/silicon/mooreslaw.h
  tm
• Van Pelt Library ENIAC Exhibit
• John W. Mauchly and the Development of the ENIAC
  Computer
• http//www.library.upenn.edu/exhibits/rbm/mauchly
  /jwm0-1.html
• Tinker Toys Website
• http//www.hasbro.com/tinkertoy/