Chapter 7

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Chapter 7 - PowerPoint PPT Presentation

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

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
• 8 million bits
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 = 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
• Binary Base 2
• Decimal Base 10
• Octal Base 8
Numbering Systems
• Why do we use the decimal system for everyday mathematics?
• 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

0000 0 0

To the chalk board...

Example Problem
• Convert the binary number 1100 1010 to decimal and hexadecimal and octal.
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

1000.111

+ 1100.011

• What 2 kinds of logic gates are needed for computer addition?
Boolean Theorems
• AA = ?
• A1 = ?
• A0 = ?
• AA’ = ?
• A’’ = ?
• A(B + C) = ?
Boolean Theorems
• A + A = ?
• A + 1 = ?
• A + 0 = ?
• A + A’ = ?
De Morgan’s Theorems
• (AB)’ = ?
• (A + B)’ = ?
• (ABC)’ = ?
• (A + B + C)’ = ?
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
• 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
• 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 7

Logic Circuits

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

A

B

Y

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

A

B

Y

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 Minutes
• What would be the truth table for the logic circuit shown 14.8(d)?

A

B

X

Y

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.