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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


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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