Boolean Algebra, Combinational Logic, Seven Segment Display, Transistors

1
Lecture 6

• Boolean Algebra, Combinational Logic, Seven
  Segment Display, Transistors

2

• Clock Generator
• Pull up/down Resistors
• Semiconductors
• Transistors
• Zener Diode
• Relays
• LED Displays
• LCD Displays
• Decade Counter
• Encoders and decoders

3
Truth tables

• See example truth tables Fig 3-40 page 49

4
Constructing circuits from Boolean Expressions

• Using Boolean algebra allows us to describe the
  desired actions of a digital system using logic
• Machine control example
• Switches (on or off)
• Left hand switch (A)
• Right hand switch (B)
• Part in place micro-switch (C)
• Tool carrier up switch (D)
• Override switch (E)

5
Constructing circuits from Boolean Expressions

• Identify switches a letters (A,B,etc)
• Identify desired result (machine on) as Y
• Describe problem in terms of words
• To start the machine, both switches must be
  pressed, and the part must be in place and the
  tool must be up.
• For maintenance, the machine can be started with
  the override switch

6
Constructing circuits from Boolean Expressions

• Write the Boolean expression for the machine
  operation in terms of the designating letters
• Y (AB C D) E

7
Drawing a circuit from a Boolean expression

• Letters (switches) to the left
• Outputs (effectors) to the right

8
Truth tables and Boolean expressions

9
Creating a Boolean expression from a Truth Table

• Write the equation for the line where Y1
• Combine the expressions with OR
• not Anot Bnot C
• Anot Bnot C
• A B not C
• not Anot B C Y

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Simplifying Boolean expressions

• Eliminating duplication
• Develop Karnaugh map
• Ordered method of grouping variables
• Circle pairs of 1s
• Simplify by excluding the duplicated variable

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Karnaugh Maps

• Four input Karnaugh map
• A not B not C not D A not B not C D
  A not B C D A not B C not D
• Five input Karnaugh map
• Two levels

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Using NAND logic

• Substitute NAND gates for each AND, OR, NOT
  (Using Table in Chapter 3)
• Simplify

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Data Selectors

• Method of dealing with complicated logic problems
• Uses an IC (DATA SELECTOR, 74150 for example)
• Output is established and then inputs are set
  using switches
• Short cut to Karnaugh map

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8421 BCD (Binary Coded Decimal) code - Gray Code
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ASCII code
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Encoders

• Code translator - Input side
• Integrated circuits that convert from a supplied
  code to the desired code
• Binary
• BCD
• Gray Code
• Excess-3
• ASCII
• Seven Segment Display

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Seven segment displays

• Seven LEDs can display numerals 0 through 9

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Seven segment displays
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Seven segment displays
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Decoders

• Code translator - Output side

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Liquid Crystal Display (LCD)

• Nematic fluid - electricity cause light to be
  reflected differently
• Appears black
• Uses a square wave
• Segments are inverted (out of phase) to produce
  black
• LCD television??

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Liquid Crystal Display

• Two metalized planes with nematic fluid between

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Chips of interest to project

• 4049 Hex buffer (Inverter)
• 4017 Johnson Decade Counter
• 4011 NAND
• 4013 Flip-Flop (Latching)

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Pull up Pull Down Resistor

• Input side of the hex inverter

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Review of project circuit