Digital Electronics: Logics and Switching Theory

• Study notes on Logics and Switching Theory, Digital Waveforms, Logic Functions, Programmable Logic Devices (PLDs), Digital Fundamentals, and Counter Circuits

Digital Electronics

• Digital electronics use circuits that have two states: HIGH and LOW.
• Digital systems process, store, and transmit data more efficiently by assigning discrete values to each point.
• Analog quantities are natural and vary continuously, handling higher power levels.

Digital Waveforms

• A digital waveform is a graphical representation of logics with respect to time. (Pulse Waveform)
• Positive Going Pulse goes from normally low logic level to a high logic level.
• Negative Going Pulse goes from normally high logic level to a low logic level.
• Actual Pulse is described by rise time, fall time, amplitude, and other characteristics. Notably, it's not ideal.
• DC Offset is a constant voltage value added to the pulse, shifting its peak.
• Pulse Width is specified by active pulse time.
  • Active High Signal: active when voltage is high
  • Active Low Signal: active when voltage is low

Basic Logic Functions

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

Basic System Functions

• Basic system functions include
  • Comparison, arithmetic, encoding, decoding
  • Data selection, counting, and shift register operations.
• Shift registers move and store data each time they are clocked

Digital System Hierarchy

• Digital systems are structured in a hierarchy
  • Levels, systems, functional units (registers, memories, arithmetic units)
  • Gates and flip-flops, electronic circuits, and components (transistors, resistors, capacitors).

Key Terms

• Analog has continuous values.
• Digital has a set of discrete values.
• Binary has two values or states, utilizing 1 and 0 as its digits.
• Bit is a binary digit (1 or 0).
• Pulse is followed by a sudden change back to the original level after a time called the pulse width.
• Clock is a basic timing signal in a digital system. It's a periodic waveform used to synchronize actions.
• Gate is a logic circuit that performs basic logic operations such as AND or OR.
• NOT performs inversion
• Fixed-function Logic circuits have functions that cannot be altered
• Programmable Logic circuits are capable of being programmed to perform specified functions
• Bit Time is the time interval occupied by each bit in a digital waveform
• Time Waveform is a graph showing the actual time relationship between two or more waveforms
• Data is a group of bits that convey some type of information
• Byte has an 8-bit
• Word is the largest data group
• The width of a single unit of data is the Word Size
• Nibble has a 4-bit group of data, or half a byte

Binary, Gray, and Alphanumeric Codes

• Binary Coded Decimal is also know as an 8421 code
• Excess-3 Code 4-bit binary coded
  • Represents each decimal character which is derived by adding (0011) with valid digits being 0011 to 1100
• Gray Code special binary code that only has a single bit that can change from one consecutive number to another
  • Used in data transmission to minimize encoding errors of a shaft encoder

Alphanumeric Binary Codes

• Alphanumeric Binary Codes are used in transmitting information via a computer
• ASCII is a 7-bit binary code with 128 characters that can use a parity bit if used in data transmission - Adopted from ANSI
• EBCDIC is an 8-bit binary code that contains 256 characters, no parity bit in data transmission
• In Binary Signed Numbers, MSB is 1 if number is negative, MSB is 0 if number is negative
• Logic Operators operate on binary values and binary variables
• Boolean Algebra provide s useful mathematical system ffor specifying and transforming logic functions
• Truth Table is atabular listing of the alues of af unction for all possible combinations of values on its arguments

Logic Gates and Operators

• Key points on logic gates and operations:
  • AND (*) - boolean multiplication
  • OR (+) - boolean addition
  • NOT (overbar, single quote, tilde) – inverter
  • NAND - inverted boolean multiplication
  • NOR - inverted boolean addition
  • XOR - inequality function
  • XNOR - defines equality function
• Gate delay (tg) is the delay between an input change and the resulting output change.
• An algebraic expression obtained by interchanging addition, multiplication. The algebraic expression also interchanging 0's and 1's
• Self Dual can only be one identity on a line
• In boolean operator precedence is PNAO - parentheses, not, and, or

Standard Order Terminology

• Standard order is defined using the following terminology:
  • Subscript referring to number corresponding to a binary pattern
  • Canonical Forms allowing comparison for equality regarding:
    • Minterms which ae AND terms (POS)
    • Maxterms being OR terms (SOP)
• Index is also used to determine whether the variable is shown in true form or complemented form:
  • Minterm definitions:
    • 1 which is not complemented
    • 0 meaning complemented -Maxterm definitions:
    • 0 meaning not complemented
    • 1 meaning complemented

Logic Simplification

• Logic Simplification Techniques include:
  • Algebraic Method which can simplify expression using boolean theorems
  • K-Map, MEV, and TABULAR Method

Evolution of Electronic Digital Devices

• Evolution of electronic digital devices has occurred in several stages
  • Individual gates using vacuum tubes and discrete passive components (resistors and capacitors)
  • Individual gates with transistors and discrete passive components
  • Integral Gate Circuits composed of several transistors and passive components fabricated in a single package, also called chips

Levels of Integrated Circuits

• Integrated Circuits are classified by their level of integration
  • Small Scale Integrated Circuits having a few gates per chip and most gate terminals available at chip pins
  • Medium Scale Integrated (MSI) Circuits with many gates and flipflops interconnected on a chip (e.g., adder or register)
  • Large and Very Large Scale Integrated (LSI and VLSI) with millions of transistors interconnected forming complete systems (e.g., microprocessors) with Moore's Law stating number of transistors that can be put on a single chip has been doubling every 1.5 or 2 years

Programmable Logic Device

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

IC Packaging

• IC Packaging includes different formats
  • Dual In-Line Packaging (DIP)
  • Surface Mount Technology (SMT)
  • PLD Programming for use in Schematic entry through Text Based Entry which can use hardware description language (HDL) like Verilog to model electronic Systems

Test and Measurement Instruments

• Instruments such as general purpose oscilloscope
• Logic analyzers which can display multiple channels of digital information or show data in tabular form
• The digital multimeter (DMM), useful for checking power supply voltages, verifying resistors, testing continuity, & making measurements

Programmable Logic (PLD)

• Programmable Logic Devices are an alternate fixed function devices, specifically Programmable Array Logic (PAL)
• PAL is form of PLD that uses a combination of AND array and a fixed OR array

Adders

• Half Adder
  • A digital circuit that adds two single binary digits (bits) and produces a sum and a carry output.
• Full Adder
  • A digital circuit that adds two single binary digits (bits) with an input carry and produces a sum and a carry output.
• Ripple Carry Adder:
  • An adder where the carry output of each full-adder (FA) connects to the carry input of the next FA.
• Look-Ahead Carry Adder:
  • An adder that calculates its carry signals in advance, based on the input signals.
• Carry Generation: Occurs when an output carry result is internally produced by a full adder
• Carry Propagation: Occurs when the input carry is rippled to become output carry.

Digital Fundamentals Glossary

• Comparators compare the magnitude of two binary quantities to determine the relationship of those quantities
  • Equality of 1-bit comparator and a 2-bit comparator
  • Inequality of 4-bit comparator
• Decoders are a digital circuit in which it detects the Specified combination of bits (code) on its inputs and indicating the presence of that code by a specified output level.
• Encoders are a combinational logic circuit that essentially performs a reverse ("reverse") decoder function
• Code converters provide BCD to Binary Conversion and Binary-Gray Conversion
• Multiplexers (Data Selectors) allow several sources to be routed onto a single line for transmission over that line to a common destination.
• Demultiplexers: takes digital information from one line and distributes it to a given number of output lines

Multiplexers and Buffers

• Parity Generator/Checker and Multibit Multiplexers are a switch allowing one of 2^n inputs to be connected to the output
• Bus is the collection of wires which form signal with the Width being number of wires in a bus
• Digital Buffer: a type of gate to isolate other gates or circuit stages from each other preventing impedance of one circuit from affecting another
• Tristate Buffer Switch is broken up between three types:
  • Active "High" Tristate Buffer
  • Active "Low" Inverting Tristate Buffer
  • Buffers increase that driving capability of a gate input with Multi-stage Buffer for high fan-out gates

Latch and FlipFlops

• Latch is a type of memory storage device that has two stable states (bistable):
  • (Level/Voltage Triggered)
• Flip-flop is also known as synchronous bistable devices, as bistable multivibrators:
  • (Edge Triggered)
• Clock is when triggering input
• Applications include:
  • Parallel Data Storage
  • Frequency Division
  • Counting

Flip-Flops and Sequential Logic

• Sequential Logic Circuits are circuits whose output depends on the sequence of inputs applied and analyzed with respect to time referring the present state and using previous state towards a next state
• Clock reference of sequential circuit operation
• The FlipFlop Operation has Delay Times between Propagation, Set up, Hold Time and a maximum clock frequency that a FlipFlop can be triggered
• The FlipFlop requires Minimum Pulse Width tw in order to be specified by the manufacture of the clock, preset and clear inputs with a minimum High time and Low time.

Flip-Flops and Power Dissipation

• Power Dissipation refers to total power conception of the device.
• Stable State the output will remain in its present state until some input change is described
• Unstable State the output will change logic state after a given time, even if the input remains unchanged
• A stable Table has feedback through process of connecting the output of the device to the input
• Sequential Circuit Triggering: Edge Triggered which can be either positive or negative
• Voltage Level Triggered

Type of Sequential Circuits

• Sequential circuits can be classified as
  • Monostable Vibrator (One Shot) is a sequential circuit with one stable and one unstable state, with it's pulse width being the amount of time in the unstable state.
  • Astable Multivibrator (Oscillator) has no stable state being either free running or gated
• Bistable Multivibrator has two stable states -Lath which uses a memory device capable of storing 1 bit of information on a voltage triggered device

Timer Operation and Flip Flops

• 555 Timer IC a linear IC capable of producing various types of oscillation timing waveforms and other digital waveform
• Schmitt Trigger Devices cause logic device to switch logic states abruptly at a specific voltage.
• Flip-flops consist of asynchronous inputs with PRE forcing output to be High and CLR forcing output to be low
• Flip Flops Types include:
  • D Flipflop uses a delay of data
  • S-R Flipflop ussa a set of a reset
  • JK Flipflop contains no invalid stat
  • T Flipflop uses a toggle

Master Salve FlipFlop

• Master Slave Flip Flop : a flipflop circuit that is pulse triggered.
• Master Slave Flip Flop is also used in:
  • D-Latch
  • S-R Latch

Counter Circuits

• Digital Counter device that generates binary number in as pecified count sequence-
• Counter Classifications:• -Count Modulus - total number of states or values generated by the counter as it progresses through its specified count sequence. -Decade Counter (MOD 10 Counters) - counters with modulus of 10. -Binary Counter - counters with n bits with modulus of 2^n

Count Types Frequency and Types

• Frequency Division which is a digital counter functioning as frequency dividers.
• Asynchronous Counters (Ripple Counter incoming clock signal is routed into the first stage of the counter which generates the LSB of the numbers in the count sequence.
• Synchronous Countersare constructed with one common clock signal as the input to all flip-flops simultaneously.
• Counter is dependent of the trigger characteristic of the flip-flops.
  • Counter Triggering can classified as positive or negative edge triggered device.
• Ring Counters (Shift Register Counters is a type of shift register and used as memory.
  • Basic Ring Counters can cycle a single logic through multiple stages of the counter Twisted Ring Counter or switch tail creates count where outputs change through consecutive states.
• Other modifiers exist such as maximum length counter that increase feed back.