Digital Electronics: Logic and Switching Theory

Digital Electronics: Logics and Switching Theory

• Analog quantities are natural and vary continuously, handling higher power levels
• Digital methods process, store, and transmit data more efficiently by assigning discrete values
• Digital Electronics uses circuits operating in HIGH and LOW states

Voltages and Binary System

• Voltages represent numbers in the binary system
• A bit (binary digit) is a single number in binary, either 1 or 0
• Digital Logic is a branch of electronics handling information in digital form

Digital Waveforms

• Positive Going Pulse transitions from a normally low logic level to a high logic level
• Negative Going Pulse transitions from a normally high logic level to a low logic level

Pulse Characteristics

• An actual pulse is described by characteristics like rise time, fall time, and amplitude
• DC Offset is a constant voltage added to a pulse to shift its peak
• Pulse Width is specified by active pulse time
• An Active High Signal is active when voltage is high
• An Active Low Signal is active when voltage is low

Digital Waveform Representation

• A digital waveform is a graphical representation of logics with respect to time

Pulses

• A Positive Pulse has a low voltage at 0 and a peak value at 1
• A Negative Pulse has a high voltage at 0 and a negative peak value at 0
• Duty Cycle is the percentage of the active pulse in a period
• A Square Wave, the most common digital waveform, has a 50% duty cycle

Periodic Pulse Waveforms

• Periodic Pulse Waveforms repeat pulses in a fixed interval called the period
• Frequency is the rate at which the pulses repeat
• A Clock is a basic timing signal and an example of a periodic wave

Timing Diagrams

• Used to show the relationship between two or more waveforms

Pulse Definitions

• A Repetitive Pulse is described by amplitude, pulse width, and duty cycle
• Duty Cycle is the ratio of pulse width to period

Serial and Parallel Data

• Serial Transfer involves transmitting data one bit at a time
• Parallel Transfer involves transmitting multiple bits simultaneously

Basic Logic Functions

• AND function is only true if all input conditions are true
• OR function is true if one or more input conditions are true
• NOT function indicates the opposite condition

Basic System Functions

• Examples include Comparison, Basic Arithmetic, Encoding, Decoding, and Data Selection Functions
• Other examples include Counting Function and Shift Register, which moves and stores data each clock cycle

Digital System Hierarchy

• Contains Levels, Systems and Functional units such as register, memories and arithmetic units
• Include Gates and Flip-flops, Electronic Circuits and Components such as transistors, resistors and capacitors

Evolution of Electronic Digital Devices

• Early individual gates used vacuum tubes and discrete passive components like resistors and capacitors
• Later individual gates used transistors and discrete passive components
• Integral Gate Circuits are composed of several transistors and passive components fabricated in a single package, known as ICs or chips

Levels of Integrated Circuits

• Small Scale Integrated Circuits have a few gates per chip, with most gate terminals available at chip pins
• Medium Scale Integrated (MSI) Circuits have many gates and flip-flops interconnected on a chip, such as adders or registers
• Large and Very Large Scale Integrated (LSI and VLSI) circuits contain millions of transistors interconnected to form complete systems, like microprocessors

Moore's Law

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

Programmable Logic Devices

• Programmable Logic Devices are integrated circuits programmed in a laboratory for complex functions
• A Field Programmable Gate Array is a gate array where the logic network can be programmed
• A Complex Programmable Logic Device is a high-density PLD containing macro cells interconnected through a central Global Routing Pool

IC Packaging

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

PLD Programming

• Schematic Entry
• Text Based Entry uses a hardware description language (HDL)
• Verilog is an HLD used to model electronic systems

Test and Measurement Instruments

• A General Purpose Oscilloscope displays electrical signals over time
• A Logic Analyzer displays multiple channels of digital information or shows data in tabular format
• DMM is useful for checking power supply voltages, verifying resistors, testing continuity, and occasionally making other measurements

Programmable Logic

• PLDs serve as alternatives to fixed function devices
• Programmable Array Logic is a form of PLD using a combination of an AND array and a fixed OR array

Key Terms

• Analog having continuous values
• Digital having a set of discrete values
• Binary having two values or states, using 1 and 0 as its digits
• Bit is a binary digit (1 or 0)
• Pulse is followed, after a time called the pulse width, by a sudden change back to the original level
• Clock is a basic timing signal in a digital system, a periodic waveform used to synchronize actions
• Gate is a logic circuit that performs basic logic operations such as AND or OR

Basic Logic Functions

• NOT is a basic logic function that performs inversion
• AND is only true if all input conditions are true
• OR is true if one or more of the inputs are true

Logic Circuits

• Fixed-function Logic uses circuits with functions that cannot be altered
• Programmable Logic uses circuits capable of being programmed to perform specified functions

Binary Codes

• Bit Time is the time interval occupied by each bit in a digital waveform
• Time Waveform shows actual time relationship between two or more waveforms
• Data is a group of bits that convey some type of information
• Byte is an 8-bit group of data
• Word is the largest data group
• Word Size is the width of a single unit of data
• Nibble is a 4-bit group of data (Half Byte)

Binary Coded Decimal

• Binary Coded Decimal is also known as 8421 code

Excess-3 Code

• Excess-3 Code is a 4-bit binary code that also represents each decimal character
• It derived by adding (0011)
• Valid digits are 0011 to 1100

Gray Code

• A special binary code that allows only a single bit to change from one consecutive number to another, useful in data transmission to minimize encoding errors
• Shaft Encoder is an application of Gray code

Alphanumeric Binary Codes

• Utilized in transmitting information via a computer

American Standard Code for Information Interchange

• ASCII is a 7-bit binary code with 128 characters, can use a parity bit if used in data transmission

Extended Binary Coded Decimal Information Code

• EBCDIC is an 8-bit binary code with 256 characters and no parity bit in data transmission

Binary Signed Number

• Most significant bit (MSB) is 1 if the number is negative and 0 if positive

Binary Logic and Gates

• Logic Operators operate on binary values and variables
• Boolean Algebra is used for specifying and transforming logic functions
• Truthtable is the listing of all value combinations

Logical Operators

• AND (*) is boolean multiplication
• OR (+) is boolean addition
• NOT (overbar, single quote, tilde) is an inverter
• NAND is inverted boolean multiplication
• NOR is inverted boolean addition
• XOR is an inequality function
• XNOR defines equality function

Gate Delay

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

Boolean Algebra

• Dual is an algebraic expression obtained by interchanging addition and multiplication and interchanging 0s and 1s
• Self Dual - only one identity on a line
• Dual expression = original expression

Boolean Operator Precedence

• PNAO parenthesis, not, and, or

Order

• Subscript number corresponding to a binary pattern
• Canonical Forms allows comparison for equality.
• Minterms AND terms (POS)
• Maxterms OR terms (SOP)
• Index used to determine whether the variable is shown in true form or complemented form

Minterm

• 1 not complemented
• 0 complemented

Maxterm

• 0 not complemented
• 1 complemented

Logic Simplification Techniques

• Algebraic Method simplifies expression using Boolean theorems
• Other methods include K-Map MEV and Tabular method

Digital Fundamentals

Comparators

• Compares the magnitude of two binary quantities to determine their relationship and if numbers equal

Types of Comparators

• Equality: 1-bit comparator and 2-bit comparator
• Inequality: 4-bit comparator

Decoders

• Digital circuit that detects the specified combination of bits (code) on its inputs and indicates the presence of that code by a specified output level

Types of Decoders

• Binary Decoder
• 4-bit decoder
• BCD-to-Decimal Decoder
• BCD-to-7 Segment Decoder

Adders

• Half Adder circuit adds two binary digits producing a sum and a carry output
• Full Adder circuit adds two binary digits and a carry-in bit, producing a sum and a carry-out bit

Ripple Carry Adder

• Carry output of each full-adder is connected to the carry of the next higher order state

Look-Ahead Carry Adder

• Anticipates the output carry of each stage based on the inputs, producing the output carry by generation or propagation

Carry Generation

• Occurs when an output carry is produced internally by the full adder, expressed as the AND function of the two input bits

Carry Propagation

• Occurs when the input carry is rippled to become the output carry, expressed as the OR function of the two input bits

Encoders

• Performs a "reverse" decoder function

Code Converters

• BCD-to-Binary Conversion and a Binary-Gray Conversion

Multiplexers (Data Selectors)

• Allows routing several sources onto a single line for transmission

Typesof Multiplexers

• 4-input multiplexers
• Extended Multiplexers

Demultiplexers

• Takes digital information from one line and distributes it to a given number of output lines

Parity Generator/Checker

• Used for error detection in data transmission

Multiplexers

• Multibit: a switch allowing one of 2^n inputs to be routed to the output and controlled by select lines

Bus

• A Bus is a collection of wires forming a signal path
• Width is the number of wires in a bus

Digital Buffer

• Used to isolate other gates or circuit stages preventing impedance issues

Tristate Buffer Switch

• Active "High" Tristate Buffer passes the input when enable is high, otherwise output is high-impedance (Hi-Z)
• Active "Low" Tristate Buffer passes the input when enable is low, otherwise output is high-impedance (Hi-Z)

Single Input Digital Buffer

• A simple digital buffer with one input and one output

Buffers

• Increase the driving capability of a gate input

Multi-stage Buffer

• Used for high fan-out gates

Latches and Flip-Flops

• Latch is a memory storage device with two stable states (bistable), triggered by level or voltage
• Flip-flop is a synchronous bistable device, also known as bistable multivibrator, edge-triggered
• Clock serves as the triggering input for flip-flops

Flip-Flop Applications

• Parellel Data Storage
• Frequency Division
• Counting

Flip-Flop Operating Delay Times

• Propagation Delay Time interval required after an input signal has been applied for the resulting output change to occur
• Set-up time minimum interval for logic levels to be maintained constantly on the input prior to triggering edge of the clock pulse
• Hold Time minimum interval is required for the logic levels to remain on the inputs after the triggering edge of the clock pulse
• Maximum Clock Frequency the highest rate at which a flip-flop can be reliably triggered
• Minimum Pulse Width is specified for the clock, preset, and clear inputs for reliable operation

Power Dissipation

• Overall number for the device

Sequential Logic Circuits

• These circuits’ output depends on the sequence of inputs applied analyzed with respect to time
• Key states include Present state, Previous state and Next State

Clock

• Reference of sequential circuit operation

Circuit

• Stable State is where the output remains in its present state until some input change
• Unstable State is where the output changes logic state after a given time, even if the input remains unchanged Feedback connects the output of the device to the input of the same device Stable Table is an organized chart used to analyze sequential circuits

Sequential Circuit Triggering

Edge Triggered

• Positive Edge
• Negative Edge

Voltage Level Triggered

Counter Circuits

• Digital Counter is a device that generates a binary number in a specified count sequence
• Count Modulus is a measure of the number of states generated as the counter progresses

Type of Counters

• Decade Counter also known as MOD 10 Counters counts to modulus of 10 states
• Binary Counter includes n bits and is known as modulus of 2^n
• Frequency Division is a digital counter that functions as frequency dividers
• Asynchronous Counters the incoming clock signal is routed into the first stage of the counter which generates the LSB of the numbers in the count sequence
• Synchronous Counters constructed with one common clock signal as the input to all flip-flops simultaneously
• Counter Triggering classified as a device depending on the trigger characteristic of the flip-flop circuits that form the counter
• Ring Counters uses special synchronous counters designed from cascaded D Flipflops that has varied patterns shifting stages
• Basic Ring Counter cycles single logic HIGH output pulse through stages of the counter by the equation; (Modulus = n)

Types of Sequential Circuits

• Monostable Vibrator (one shot) is a sequential circuit with stable and unstable states
• Pulse width is the time the one shot is in its unstable state
• Astable Multivibrator (Oscillator) has no stable state

555 Timer IC

• 555 Timer IC is a linear IC producing types of oscillation timing waveforms

Schmitt Trigger Devices

• Causes logic device to switch abruptly at a specific voltage

Bistable Multivibrator

• Has two stable states
• Latch is a memory device capable of storing 1 bit of information and voltage triggered device

Flip-Flops Asynchronous Inputs

• PRE forces output to be high (1)
• CLR forces output to be low (0)

Types of Flip-Flops

• D Flipflop the delay or data flipflop
• S-R Flipflop set-reset flip-flop
• JK Flipflop no invalid state
• T Flipflop- Toggle flipflop
• Master Slave Flipflop a flipflop is pulse triggered

Twisted Ring Counter

• Twisted Ring Counter generates a count sequence with only one output changing between consecutive count states is
• (Modulus = 2n)
• Modified Twisted Ring Counter has a similar twisted ring less one output state the equation is
• (Modulus = 2n-1) Maximum Length Counter which requires a more complex feedback circuitry, the equation is
• (Modulus = 2^n-1)