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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
- Hexadecimal Base 16
- Octal Base 8

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

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

- Add these binary numbers:

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.

Exercises

- P7.19
- P7.20
- P7.21,22,23

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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