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Chapter 7. Logic Circuits. Positive Logic. Logic 1 high, true, on 5 Volts Really: 2.4 to 5 Volts Logic 0 low, false, off 0 Volts Really: 0 to 0.4 Volts Logic X “don’t care” Really: 0.4 to 2.4 Volts. Binary Numbers. Bit a single binary digit Byte 8 bits Nibble 4 bits Megabyte

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chapter 7

Chapter 7

Logic Circuits

positive logic
Positive Logic
  • Logic 1
    • high, true, on
    • 5 Volts
      • Really: 2.4 to 5 Volts
  • Logic 0
    • low, false, off
    • 0 Volts
      • Really: 0 to 0.4 Volts
  • Logic X
    • “don’t care”
    • Really: 0.4 to 2.4 Volts
binary numbers
Binary Numbers
  • Bit
    • a single binary digit
  • Byte
    • 8 bits
  • Nibble
    • 4 bits
  • Megabyte
    • 8 million bits
transmission of digital information
Transmission of Digital Information
  • Parallel Transmission
    • an n-bit word is transferred on n wires plus a common or ground wire
  • Serial Transmission
    • the successive bits of a word are transferred one after another with a single pair of wires
ttl logic circuits
TTL Logic Circuits
  • TTL = Transistor-Transistor Logic
  • Logic Gates
    • AND
    • OR
    • NOT (inverter)
    • NAND
    • NOR
    • XOR
    • Equivalence Gate
    • Buffer

Circuit Symbol

Truth Table

Boolean Expression

Multiple Inputs

numbering systems
Numbering Systems
  • Binary Base 2
  • Decimal Base 10
  • Hexadecimal Base 16
  • Octal Base 8
numbering systems1
Numbering Systems
  • Why do we use the decimal system for everyday mathematics?
    • Answer: Fingers and Thumbs
  • Why do we use the binary system for computer mathematics?
    • Answer: Computers use voltage levels to perform mathematics.
    • 0-Volts and 5-Volts correspond to 0’s and 1’s
counting
Counting

Binary Decimal Hexadecimal

0000 0 0

To the chalk board...

example problem
Example Problem
  • Convert the binary number 1100 1010 to decimal and hexadecimal and octal.
more examples
More Examples
  • Convert 34310 to binary and hexadecimal and octal.
  • Convert 1101.12 to decimal an octal.
  • Convert 0.39210 to binary.
  • Convert 317.28 to binary.
exercises
Exercises
  • Add these binary numbers:

1000.111

+ 1100.011

  • What 2 kinds of logic gates are needed for computer addition?
boolean theorems
Boolean Theorems
  • AA = ?
  • A1 = ?
  • A0 = ?
  • AA’ = ?
  • A’’ = ?
  • A(B + C) = ?
boolean theorems1
Boolean Theorems
  • A + A = ?
  • A + 1 = ?
  • A + 0 = ?
  • A + A’ = ?
de morgan s theorems
De Morgan’s Theorems
  • (AB)’ = ?
  • (A + B)’ = ?
  • (ABC)’ = ?
  • (A + B + C)’ = ?
7 4 synthesis of logic gates
7.4 Synthesis of Logic Gates
  • Find the sum-of-products for G for the truth table in Table P7.35 on page 370.
  • Can the equation be simplified?
  • If so, how many gates did we save?
  • Repeat for Table 7.7.
7 5 minimization of logic gates
7.5 Minimization of Logic Gates
  • Find the sum-of-products for the truth table in Table 7.8 on page 352.
  • Can the equation be simplified?
  • How many gates did we save?
  • Is there a easier way to simplify these equations?
karnaugh mapping steps
Karnaugh Mapping Steps
  • Sketch a Karnaugh map grid for the problem.
  • Fill in the 1’s and 0’s from the truth table.
  • Circle groups of 1’s.
  • Write an equation using these circles.
chapter 71

Chapter 7

Logic Circuits

Reminder: Remember to keep your graded labs for your lab portfolio.

example problem1
Example Problem
  • What would be the truth table for the logic circuit shown in figure 4.18(a)?

A

B

Y

example problem2
Example Problem
  • What would be the truth table for the logic circuit shown 14.8(b)?

A

B

Y

team exercise 4 minutes
Team Exercise – 4 Minutes
  • What would be the truth table for the logic circuit shown 14.8(c)?

A

B

X

Y

team exercise 4 minutes1
Team Exercise – 4 Minutes
  • What would be the truth table for the logic circuit shown 14.8(d)?

A

B

X

Y

exercises1
Exercises
  • P7.19
  • P7.20
  • P7.21,22,23
slide36

Lenz

Karnaugh

Zener

Mosfet

Thevenin

Kirchhoff

Coulomb

Boolean

Note: These are the assigned teams for the SFA Rover project. Teams were assigned alphabetically and by lab section.

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