• Digital electronics involves logic and switching theory.

Analog vs. Digital

• Analog quantities are natural, vary continuously, and can handle higher power levels.
• Digital systems process, store, and transmit data more efficiently by assigning discrete values.

Digital Electronics Basis

• Digital electronics uses circuits with two states: HIGH and LOW.
• Logic levels corresponds to voltage ranges, with invalid ranges in between.

Key Definitions

• Bit (Binary Digit): A single number in binary (1 or 0).
• Digital Logic (Digital Electronics): Branch of electronics using digital representation.

Digital Waveforms

• Digital waveforms graphically represents logic levels over time.
• Positive-Going Pulse: Transitions from low to high logic level.
• Negative-Going Pulse: Transitions from high to low logic level.
• Pulses characterized by rise time, fall time, amplitude and other characteristics. (not ideal)

Digital Signals

• DC Offset: Constant voltage added to shift the pulse's peak.
• Pulse Width: Defined by active pulse time.
• Active High Signal: Active when voltage is high.
• Active Low Signal: Active when voltage is low.

Waveform Characteristics

• Positive Pulse: Low voltage at 0, peak at 1.
• Negative Pulse: High voltage at 0, negative peak at 0.
• Duty Cycle: Percentage of active pulse in a period.
• Square Wave: Common digital waveform with 50% duty cycle.

Periodic Pulse Waveforms

• Periodic pulse waveforms repeat at a fixed interval (period).
• Frequency: Rate at which the waveform repeats.
• Clock: Basic timing signal and a periodic wave example

Timing Diagrams

• Timing diagrams shows relationship between multiple waveforms.

Pulse Definitions

• Repetitive Pulse: Described by amplitude, pulse width, and duty cycle.
• Duty Cycle is a ratio of pulse width to period.

Data Transmission

• Serial Transfer: Data transmitted one bit at a time.
• Parallel Transfer: Multiple bits transmitted simultaneously.

Basic Logic Functions

• AND: True only if all inputs are true.
• OR: True if one or more inputs are true.
• NOT: Indicates the opposite condition (inversion).

Basic System Functions

• Comparison
• Basic Arithmetic
• Encoding
• Decoding
• Data Selection
• Counting
• Shift Register (moves and stores data with each clock)

Digital System Hierarchy

• Levels
• Systems
• Functional units (registers, memories, arithmetic units)
• Gates and Flip-flops
• Electronic Circuits
• Components (transistors, resistors, capacitors)

Evolution of Electronic Digital Devices

• Individual Gates (vacuum tubes, discrete passive components)
• Individual Gates (transistors, discrete passive components)
• Integral Gates Circuits (transistors, passive components in single package, ICs or chips)

Levels of Integrated Circuits

• Small Scale Integrated Circuits: Few gates per chip, most gate terminals accessible.
• Medium Scale Integrated (MSI) Circuits: Many gates and flip-flops interconnected on a chip.
• Large and Very Large Scale Integrated (LSI and VLSI): Millions of interconnected transistors forming complete systems.

Moore's Law

• The number of transistors on a single chip doubles roughly every 1.5 to 2 years.

Programmable Logic Devices (PLDs)

• PLDs are integrated circuits that can be programmed in a lab.
• Field Programmable Gate Array: Gate array programmed for logic networks
• Complex Programmable Logic Device: High-density PLD with macro cells connected through a Global Routing Pool.

IC Packaging

• Dual In-Line Packaging (DIP)
• Surface Mount Technology (SMT)

PLD Programming

• Schematic Entry: Uses graphical representation for design.
• Text Based Entry: Uses hardware description language (HDL).
  • Verilog is an HDL used to model electronic systems.

Test and Measurement Instruments

• General Purpose Oscilloscope displays signals
• Logic Analyzer: Displays multiple digital information channels in tabular form.
• DMM: Checks power supply, voltages, resistors, continuity, and other basic measurements.

Programmable Logic

• PLDs: Alternative to fixed-function devices.
• Programmable Array Logic (PAL): Form of PLD using AND array and fixed OR array.

Key Terms

• Analog: Continuous values.
• Digital: Discrete values.
• Binary: Two values/states (1 and 0).
• Bit: Binary digit (1 or 0).
• Pulse: Sudden level change followed by return to original level.
• Clock: Basic timing signal to synchronize actions.
• Gate: Logic circuit for basic operations like AND or OR.
• NOT: Logic performing inversion
• AND: True only if input conditions are true
• OR: True if one or more inputs are true.
• Fixed-function Logic: Unalterable circuits.
• Progammable Logic: Circuits can be programmed

Binary Codes

• Bit Time: Duration of bit in digital waveform.
• Time Waveform: Graph of relationship between 2+ waveforms
• Data: Group of bits that convey information.
• Byte: 8-bit data group.
• Word: Largest data group.
• Word Size: Width of data unit.
• Nibble: 4-bit group (Half byte).

Binary Coded Decimal (BCD)

• Also known as 8421 code.

Excess-3 Code

• 4-bit binary code for decimal characters, derived by adding (0011)
• Valid digits range from 0011 to 1100.

Gray Code

• Special code with single bit change between consecutive numbers which minimizes data transmission errors
• Shaft Encoder: Typical gray code application.

Alphanumeric Binary Codes

• Used for transmitting information via a computer.
• ASCII : 7-bit code (128 chars), used for data transmission adopted from ANSI
• EBCDIC: 8-bit code (256 chars), no parity bit in data transmission

Binary Signed Number

• MSB is 1: Number is negative.
• MSB is 0: Number is positive.

Binary Logic and Gates

• Logic Operators: Operates on binary values/variables.
• Boolean Algebra: System for specifying and transforming logic functions.
• Truth Table: Tabular listing of values for function argument combinations

Logical Gates

• AND (*): Boolean Multiplication
• OR (+): Boolean addition
• NOT: Inverter
• NAND: Inverted boolean multiplication
• NOR: Inverted boolean addition
• XOR: Inequality function
• XNOR: Equality function

Gate Delay(tg)

• Gate delay is delay between the resulting output change and an input change

Boolean Algebra

• Dual: Algebraic expression,interchange addition/multiplication and 0s/1s
• Self Dual: Identity is on a line. Dual expression = original expression

Boolean Operator Precedence

• (PNAO) - parentheses, not, and, or

Standard Order

• Subscript: Number corresponding to a binary pattern.
• Canonical Forms : Allows comparison for equality.
  • Minterms: AND terms (POS)
  • Maxterms: OR terms (SOP)
• Index Determines if variable shown as true or complemented form
• Minterm: 1 - not complemented 0 = complemented
• Maxterm: 0 = not complemented 1 = complemented

Logic Simplification Techniques

• Algebraic Method simplifies expressions using Boolean theorems
• K-Map
• MEV
• Tabular Method

Digital Fundamentals

• Comparators: Compares two binary values to determine the mathematical relations

Adders

• Half Adder: adds two bits, producing a sum and carry-out.
• Full Adder: adds 3 bits (two input bits and a carry-in), producing a sum and carry-out.
• Ripple Carry Adder: carry output of each full-adder connected to the carry input of next stage
• Look-Ahead Carry Adder: Anticipates carry output of each stage. Uses carry generation or carry propagation
• Carry Generation: Occurs when an output carry produced internally by the full adder

Decoder Definition

• Digital circuit detecting code in certain combination of bots and indicates the presence of that code at specific output level
• Examples: Binary decoder, 4-bit decoder, BCD-to-Decimal and BCD-to-7 segment

Encoders

• Performs reverse decoder function using combinational logic circuit

Code Converters

• Conversion between Codec such BCD to Binary, Binary to Gray

Multiplexers (Data Selectors)

• Allows several sources into a single transmission line to common destination
• Examples: 4-input, Extended Multiplexers

Demultiplexers

• Takes digital information from one line giving it to set number of output lines

Multiplexer Function

• Parity Generator/Checker: Checks parity of digital data

Multiplexing

• Multibit Multiplex: Switch connecting 2^n inputs to the output
• Bus: Collection of wires forming a signal. Width specifies number of wires in the bus.
• Digital Buffer isolates gates/circuits, preventing impedance affecting another circuit.

Tristate Buffer Switch Definition

• Active "High" Tristate Buffer: Output enabled when control signal is high.
• Active "Low" Tristate Buffer: Output enabled when control signal is low.

Buffer Types

• Digital Buffer: Output is the same as input when enabled.
• Buffers: Increase driving capability of gate input
• Multi-stage Buffer: High fan-out rates

Latch And Flip-Flops

• Latch: Memory storage devices that has two stable states, level/voltage triggered
• Flip-Flop: Synchronous bistable devices (bistable multivibrators), edge triggered
• Clock: Triggers input

Flip-Flop Timing

• Propagation Delay Time: Time range after input signal applied and the resulting output change
• Set-up Time (ts): Minimum range which the logic levels can occur at the input prior triggering edge of clock pulse
• Hold time (th): Minimum range the logic levels have to remain on the input after triggering edge of clock pulse
• Maximum Clock Frequency: The highest rate a flip flop can still be reliable
• Minimum Pulse width (tw): Specified manufacturer for preset ,clock clear, etc to maintain reliable operation

Flip-Flop Devices

• Power dissipation is total power consumption
• Parallel data storage, Counting, and Frequency division

Sequential Logic Circuits

• Their output depend input sequences/ analyzed by the time - Present ,previous, and next states
• Flip-flops operate based on reference in sequential circuit operation
• Stable State The output still stays its present rate until input change is described.

Feedback

• Connecting the output of the device to the input
• Stable table is a truth table used to examine sequential circuits

Sequential triggering

• Edge and voltage level triggered

Sequential Circuits

• Monostable Vibrator (one shot): Sequential circuit with one stable and one unstable form
  • Pulse width -time the one shot is in its unstable state and non/retriggerable
• Astable Multivibrator (Oscillator): Doesn't have a stable rate
  • Gated and fre-running
• 555 Timer IC : Linear IC for oscillation timing waveform
• Schmitt Trigger Devices: Causes devices to rapidly switch at specific voltages
• Bistable Multivibrator: Memory device storing 1 but of information
  • Voltage Triggered D-Latch and S-R Latch
• Asynchronous Flip-Flop Inputs : force high/low with PRE/CLR

Flip-Flop Device

• Types: D, S-R, JK, T flip-flops and a master-salve as well

Counter Circuits

• Device generating binary number in specified count sequence
• Count modulus, Decade and binary counters

Frequency Counter

• DIV counter and digital counter function on same rate
• Clock is routed to the first state of counter w/ asynchronous and synchronous counter

Counter Triggering

• Device is classified after edge and flip-flop circuits

Ring and Twisted Counter

• Used in asynchronous circuits with D Flip-Flops by shifting bit patterns
• Types
  • Basic :HIGH output pulse shifts through counter (Modulus =n)
  • Twisted: Output changes, consecutive with switch tail/Johnson/moebus
  • Modifies Twist: similar but with 1 less output

Maximum Length Counter

More complex circuitry is require