LOGIC GATES

Digital Logic

•Introduction, Truth Tables and Boolean expressions
•Logic Gates
•Combination of Logic Gates
•Circuit tracing and Boolean expressions
•Creating Truth Table from a circuit
•Creating a Circuit from a Truth Table
•Basic Boolean Algebra
•Using Boolean Algebra for Circuit Simplification
•Practical Considerations

Digital Circuit versus an analog circuit
•Digital systems operate based on discrete information or signals, were as an analog system relies on continuous information or signals. •Digital systems are binary in nature, they have two distinct states as opposed to the infinite states available in an analog system.
•A Digital system accepts discrete inputs and generates discrete outputs, such as On/Off, High/Low, True/False, or 1/0.
EXAMPLE 7.1

Car
Seat

Pressure
Sensor

Comparator

Enable
Accelerator
Seat
Belt

Voltage
Sensor

Possibilities: Y or N
Pressure

Comparator

A

Voltage Run

F=

B

F

Function of Truth Tables and Boolean expressions
Inputs
A
B
C

Output

Digital
Circuit

A Truth Table is used to describe the relationships of inputs and outputs in tabular form.
Input Combinations

Output

A B

C

F

0
0
0
0
1
1
1
1

0
1
0
1
0
1
0
1

1
0
0
1
1
0
1
0

0
0
1
1
0
0
1
1

F

A Boolean expression can be used to describe the relationships of inputs and outputs in mathematical form. F = A’B’C’+A’BC+AB’C’+ABC’

Logic Gates
Digital logic circuits consist of a series of special integrated circuits called “gates.”
The gates are the building blocks of the circuit and can be combined to construct a circuit to satisfy practically any situation.
We will cover the gates known as:
NOT gate (or inverter)
AND gate
OR gate
NAND gate
NOR gate
XOR gate (exclusive OR gate)

NOT gate (inverter)

The simplest of all logic gates

A

A’

A F = A’
0
1
1
0

Note we will use A’ to represent the complement of A or any