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Digital Electronics
Most modern electronic devices such as mobile telephones and computers depend on
Digital Logic
A name given to electronic circuits that use discrete voltage levels and modeled by logic expressions
Building Blocks
These circuits are the _____ blocks of computers and other devices
Signals
Used to transmit information, usually through electric signals
Analog Signal
Digital Signal
Two types of signals:
Analog Signal
Continuous signal for which the time varying feature of the signal is a representation of some other time varying quantity
Microphone
Speakers
Examples of Analog Signal:
Analog Technology
Is cheaper but there is a limitation of size of data that can be transmitted at a given time
Digital Signal
Uses discrete (discontinuous) values
Digital Technology
Data is converted into binary code and then reassembled back into original form at reception points
Computers
CD
DVD
Examples of Digital Signal:
Digital System
Uses digital circuits that process digital signals which can take on one of two values, 0 and 1
Microprocessors
Contain several functional and control units
Logic Gates
Make up functional and control units
Transistors
Are used to build logic gates
Transistors
A semiconductor device used to amplify and switch electronic signals and electrical power
Number System
Consists of an order set of symbols (digits) with relations defined for operators
Radix or base
_____ of the number system is the total number of digits allowed in the number system
Positional Number Systems
A number is represented by a string of digits, where each digit position has an associated weight
Binary Logic
A type of logic where variables are represented by only two states or values: 0 and 1
Binary Logic
Used extensively in computer systems, digital circuits, and programming because computers operate using binary
Boolean Algebra
A mathematical system for working with binary variables and logical operations
Boolean Algebra
The foundation of modern digital logic
George Boole
Boolean algebra is developed by who
1850s
Boolean algebra is developed during
Binary Variables
Variables that can take only one of two values, 0 or 1
Operators
Used to perform logical operations on binary values
AND
OR
NOT
Three basic logical operators:
AND
The output is 1 (True) if both inputs are 1; otherwise, the output is 0
OR
The output is 1 if at least one input is 1; the output is 0 only if both inputs are 0
NOT
Inverts the input: 0 becomes 1, and 1 becomes 0
Truth Table
A table that shows all possible values of binary variables and their corresponding output for a logical operation
Truth Table
Helps visualize how different combinations of binary values affect the result of a logical operation
NAND
Output is 1 if at least one input is 0
NOR
Output is 1 only if both inputs are 0
XOR
Output is 1 if exactly one of the inputs is 1
Laws of Boolean Algebra
A set of rules and properties used to simply and manipulate boolean expressions in digital logic and computer science
Boolean Algebra
A system of algebra that deals with binary variables and logical operations
Boolean Algebra
A powerful tool for simplifying and analyzing digital circuits
Boolean Algebra
Its built upon foundational laws which govern how boolean variables interact under logical operations
Boolean Functions
Maps input variables to output variables, using boolean operations
Truth Tables
These tables visually represent the output of a boolean function
Canonical Forms
These forms ensure every possible input combination has a unique output, offering a structured way to represent boolean functions
Standard forms
Simplify complex expressions, minimizing the number of gates needed to implement a function, thereby optimizing circuit design
Encrypted
Digital can be _____ so that only the intended receiver can decode it
Accuracy
Advantage of digital systems over analog systems is the _____ of results
Reliable
More ____ than analog systems due to better immunity to noise
Ease of design
No special math skills needed to visualize the behavior of small digital circuits
Speed
A digital logic element can product an output in less than 10 nanosecond (10-8 second)
Economy
Digital signals can be processed by digital circuit components, which are cheap and easily produced in many components on a single chip
Flexibility and Functionality
Advantage of digital systems over analog systems are ____ and ____
Logic Gates
Physical devices that implement logical operations in hardware
Decision Making in Programs
Conditional statements (if-else) use binary logic
Digital Circuits
Microprocessors, memory units, and other hardware use binary logic for operations
Networking Protocols
Binary logic helps in error checking and data transmission protocols
