Lecture 1 Flashcards
Digit
Any of the Arabic figures of 1 through 9 and 0
Any of the symbols of other number systems, as 0 or 1 in binary
Digital
Implies that all values in the system are fully represented by a series of digits
Of, relating to, or using data in the form of numerical digits (image)
Involving or using numerical digits expressed in a scale of notation, usually in the binary system, to represent discretely all variables occurring in a problem
Analog
Of or relating to a mechanism that represents data by measurement of a continuous physical variable, as voltage or pressure
The world is ____
Analog
All analog observations have ____ possibilities
Infinite
____ values simplify to a discrete or finite realm
Digital
Limited set of values for an observation
Creating a digital signal from an analog signal
Quantize the analog signal, rounding all continuous values to the closest integer
Digital, discrete-time signal
May be produced by an analog-to-digital converter (ADC)
Digital systems
Inputs and outputs are both digital, discrete-time signals
Represents information with discrete-valued variables, variables with a finite number of distinct values
Why use digital signals at all?
So that signal processing can be implemented on a digital computer (operate on 1’s and 0’s)
Digital signals are more immune to noise interference than their analog counterparts
Disadvantages of digital signals
Reduces accuracy, adds additional components (ADC)
Digital systems advantages
Building blocks are simple (1’s and 0’s)
Designer’s challenge is to combine these simple blocks into complicated systems
Microprocessor is an example of a digital system that is too complex to understand all at once
Advances in microprocessors have:
Made cell phones and internet possible
Vastly improved medicine
Managing complexity
Abstraction, discipline, and the 3-Y’s (hierarchy, modularity, regularity)
Abstraction
Hiding details when they are not important
The lowest abstraction level
Physics (motion of electrons)
Behavior of electrons is determined by
Quantum mechanics and Maxwell’s equations
Our system is constructed from ____ such as transistors (once, vacuum tubes)
Electronic devices
Terminals
Well-defined connection points in devices
Can be modeled by the relationship between voltage and current as measured at each terminal
Device level
Can ignore individual electrons
Transistors, diodes
Analog circuits level
Devices are assembled to create components such as Amplifiers, filters
Input and output a continuous range of voltages
Digital circuits level
AND gates, NOT gates
Restrict the voltages to discrete ranges, which we use to indicate 0 and 1
Logic level
Adders, memories
Micro-architecture level
Datapaths, controllers
Combining logic elements to execute the instructions defined by the architecture
Architecture level
Instructions, registers
Describes a computer from the programmer’s perspective
Operation systems level
Device drivers
Handles low-level details such as accessing a hard drive or managing memory
Application software level
Programs
Uses these facilities provided by the operating system to solve a problem for the user
Abstraction levels
Application software Operation systems Architecture Micro-architecture Logic Digital circuits Analog circuits Devices Physics
Discipline
The act of intentionally restricting your design choices so that you can work more productively at a higher level of abstraction
Digital circuits
Hierarchy
Dividing a system into modules, then further subdividing each of these modules until the pieces are easy to understand
Breaking up into components, and describing lower-level components in detail
Modularity
Giving modules well-defined functions and interfaces, so that they connect together easily without unanticipated side effects
Dictates that there should be no side effects
Regularity
Ensuring uniformity among modules so that common modules can be reused many times, reducing the number of distinct modules that must be designed
Teaches that interchangeable parts are a good idea
Charles Babbage’s Analytical Engine
1834-71
Mechanical computer that used variables with 10 discrete values
Used gears with 10 positions labeled 0 through 9
Each row in the engine processes one digit
25 rows of gears, so 25-digit precision
Binary representation
High voltage - 1
Low voltage - 0
Most electronic computers use this because its easier to distinguish between 2 voltages than 10
A binary variable conveys…
1 bit of information
Bit
Short for binary digit
A continuous signal theoretically contains ___ amount of information
Infinite
Boolean logic
Created by George Boole (1815-64)
TRUE (1, HIGH) or FALSE (0, LOW)
Digital abstraction
Allows digital designers to focus on 1’s and 0’s, ignoring whether the Boolean variables are physically represented by: specific voltages, rotating gears, hydraulic fluid levels
A programmer can work without needing to know the intimate details of the ____
Computer hardware (HW)
Understanding these HW details allows the programmer to optimize the software (SW) better for that specific compiler
An individual bit carrier very little information
We use number systems to group bits together to represent numbers
Groups of bits can also represent letters and programs
Supply voltage
The highest voltage comes from the power supply (Vdd)
The lowest voltage in the system is ___
0V (ground or GND)
In 70’s-80’s tech, Vdd was
5V
As chips have progressed to smaller transistors, Vdd has dropped to
3.3V, 2.5V, 1.8V, 1.5V, 1.2V, or lower to save power and avoid overloading the transistors
The mapping of a continuous variable onto a discrete binary variable is done by defining
Logic levels
Defining logic levels
1st gate - driver
2nd gate - receiver
Output of driver connected to input of receiver
Driver produces a 0 output in range of 0 to Vol or a high output in range 0 to Voh to Vdd
If the receiver gets an input in the range 0 to Vil
Input LOW
If the receiver gets an input in the range Vih to Vdd
Input HIGH
If, due to noise or faults, the receiver’s input falls in the forbidden zone, the behavior of the gate is
Unpredictable
Forbidden zone
Between Vil and Vih
For output of driver to be correctly interpreted at input of receiver, we must choose…
Vol < Vil and Voh > Vih
Noise margin
Amount of noise that could be added to a worst-case output such that the signal can still be interpreted as a valid input
