Counting in 1s and 0s and Logic Gates

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Counting in 1s and 0s and Logic Gates

• GEMS Seminar 1
• April 7, 2005
• Presenter Ana Maria

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Topics of Discussion

• Learning how to count in 1s and 0s
• Writing Our Names in 1s and 0s using ASCII
• What is an AND, NAND, OR, NOR Gates
• Further Applications
• Questions and Answers

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Logic Circuits

• So what Reads these 1s and 0s?
• Logic Gates starting from the fundamental Gates
  of AND, OR, NOT.and so forth. Having a series of
  combinations of these create latches and bigger
  systems.

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Majors Using this Knowledge

• Computer Engineering Combine aspects of Computer
  Science and Electrical Engineering, creates the
  bridge between the software and hardware.
• Electrical Engineering, deal with the hardware,
  responsible for the little components inside a
  computer
• Computer Science, are programmers who deal with
  the softwaretell computers what to do.

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Websites to Visit

• Animation of AND and OR Gates
• www.acad.humberc.on.ca/ ceng103/logic2.html
• Using AND and OR Gates to Turn on Lights
• www.technologystudent.com/ elec1/dig2.htm

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What Base do we count in?

• We count in base 10.
• 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
• 11-Notice how the 1 in the 10ths place will not
  increment until it reaches 10 once more) 12, 13,
  14, 15, 16, 17, 18, 19
• 20( it Changed!!!)

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What base do computers count in?

• Computers count with 1, 0s that is called binary
  (bin-meaning 2). AMAZING!
• Computers transmit data in strings of 1s and 0s
  called bits
• We only use the numbers 1, 0 with a base of 2.

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What is Base 2?

• Binary has a base 2, the only number that changes
  is the exponent
• Baseexponent 201n.
• 20 1 , 21 2,
• 22 2x2 4, 23 2x2x2 8

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Creating the Number 9

• How do you create the number 9 in Binary?
• 81 9, 54 9
• 72 9, etc.
• The one we can represent is 8 1 9
• Given 4 places.

• ___ ___ ___ ___
• 8 4 2 1
• 8 0 0 1
• 1 0 0 1

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Closer Look into Binary

• Creating the Number 1

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Lets try some Problems

• What is the number 8 in binary?
• What is the number 5 in binary
• What is the highest number using 4 digits?

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Lets try some Problems

• What is the number 8 in binary?
• _ _ _ _
• 8 4 2 1
• In Binary 1000
• What is the number 5 in binary
• _ _ _ _
• 8 4 2 1
• In Binary 0101
• What is the highest number using 4 digits?
• _ _ _ _
• 8 4 2 1
• In Binary 1111 In base 10 15

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Activity

• Write your neighbors first name or their nick
  name in binary using the ASCII Table
• Ana 0100001 01101110 0110001
• Hana 01001000 0100001 01101110
  0110001
• Bev 01000010 01100101

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The TRUTH about AND

• We analyze gates in terms of truth tables
• Multiplying (x, , /\)
• is the same as ANDING the result is AB
• We Use variables like A, B as the inputs
• AND Gates require both to be 1

Truth Table INPUTS OUTPUTS
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The Truth About OR GATES
Truth Table INPUTS OUTPUTS

• An OR gate will be on if, at least one of them is
  High that is 1.
• We used the symbol ( , \/ ) to indicate an or
  operation.

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NOT, INVERTER

• The Inverter Gives the exact opposite of what is
  put in.
• You Put a Low (0) it will give you a High (1)
• The Sign of inverting is an apostrophe or a bar
• A
• or _
• A

Truth Table INPUTS OUTPUTS
Inverter                                      
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So, What happens when you NOT an AND?

• You will get a NAND GATE!!!
• Your result will have all the original AND
  outputs Inverted.

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Truth Table and NAND Diagram
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SoWhat about an Inverted OR?

• Try it yourself
• What do you think its called?
• GOOD JOB!!

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Truth Table of Inverted OR

• What do you think its called?
• A NOR
• GOOD JOB!!

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Truth Table and OR Diagram
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FUN WITH GATES

• Line Up in Groups of 4
• 2 People are the INPUTS
• 1 Person is the OUTPUT
• 1 Person is the INVERTER

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Rules of the GAME

• There are two Lines
• Duck to represent low (0)
• Stand tall to represent High(1)
• The Inverter person has to tap the other people
  to put them in the correct position.
• Make the following configurations of Gates!

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MAKING AND and OR Gates

• MAKE the Truth Table of the AND Gate
• Try Inputs 00, 01, 10, 11
• Make the Truth Table of the OR gate
• How about the NAND and the NOR?

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Questions?

• I might be able to answer some questions, but
  write them down and Ill get the answer for you
  by next seminar!
• ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

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THANKS For Your Attention!!

• We will be taking a 10min break then talk to
  someone over the AG..
• Be back in 10 Please! ?