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information
some knowledge you want to record or transmit
ex. personâs weight, current time, picture of a cat
data
the representation of the above
personâs weight
63kg, 139 lbâŠ
one average goat
time
13:34:16, 1:34:16PM
signal
some means to record or transmit data or information
voltage, current, handwritten note, markings on wood
Inherently continuous (with infinitely many values in any range)
mass
temperature
most other physical quantities (ex. body temperature, blood pressure)
Inherently discrete (with finite number of values in any range)
days in a week
current study term
names of the cities
number of steps walked
number of students on campus today
text or any other typed or written symbols
2 main ways to represent information:
Analog data
digital data
analog data
continuous representation, analogous to the actual information it represents
digital data
discrete representation, using a finite number of digits (or any other set of symbols) to record the information
spirit (or mercury) thermometer exemplifies ______ information display where the liquid level ___________ rises and falls in direct proportion to the temperature
analog; continually
_________ displays only show (represent) information in a ________ fashion
digital; discrete
mercury (Hg) sphygmomanometer
extremely accurate
uses toxic metal
aneroid sphygmomanometer
less accurate
non-toxic
digital sphygmomanometer
pretty accurate
very easy to use
all three measure a continuous physical property: pressure
representation is different: heigh of a Hg bar, angle of the needle, number on a display
a continuous property (information), various digital representation (data); some information is allowed to be lost in the representation process
how much you read
performance in a course
continuous data represented in a discrete way
computers are finite
information often possesses an infinite range of values
ex. how many real numbers between 0 to 1
however computers are finite and also deterministic (ie. not random)
they can only operate on a fixed amount of data at a time
the amount and type of data must be known ahead of time
how can we represent information from infinite range?
represent enough of the range to meet our computational needs
2-Step analog to digital data conversion
sampling (discretization)
converts continuous variation to discrete snapshots
examples: digitalization of video; dividing still picture into pixels; digitalization of audio
quantization (truncation)
converts an infinite range of values to a finite one
examples: 1/3, pie, root 2 (making an approximation)
discretization of continuous variation by sampling
sampling an analog signal: the continuous signal is represented with a green coloured line; the discrete samples are indicated by the blue vertical lines. Signal values between samples are discarded during this process
information can be lost
we decide what can be lost at the very beginning
there are mechanisms to determine proper parameters to digitize analog data (continuous information) with as much precision as necessary
NyquistâShannon sampling theorem
quantization error models
any losses are completely avoidable after digitization is performed
bites and bytes
the basis for representing digital data is the binary digit (bit), with the unit symbol b
a bit holds one of two values: 0 or 1
often combined in groups of eight to represent data
a group of 8 bits is called a byte, with the unit symbol B
can be combined with metric prefixes for larger magnitudes
Eg. âMbâ for megabit and âMBâ for megabyte
decimal multipliers
communication (gigabit ethernet: 1 billion per sec)
data transfer
clock rates
storage, by manufacturers
storage, by some operating systems
DVDs
binary multipliers
memory capacity
storage, by some operating systems
CDs
why digital and why binary?
computers cannot work well with analog data
discretize the data (ie. breaking it into discrete samples)
quantize the values (or approximate the quantities)
benefits of digital in signal transmission (and storage)
analog signals have continuous values (fluctuate in the value range)
digital signals have only a high (1) or low (0) state - if binary; or small number of easily distinguishable states otherwise
when transmitted, all electronic signals (both analog and digital) degrade as they travel from transmitter to receiver
the level of the signal fluctuates due to ânoiseâ produced by external affects
similar effects at play when the signals are recorded
analog and signal transmission
degradation of analog signals is permanent; there is not way to determine if the distortion was not present originally
digital and signal transmission
if the distortion is small enough, can completely regenerate the signal and regain its original shape
benefits of digital for storage and compression
both digital and analogue data can be recorded
magnetic audio tapes, vinyl records, pencil drawings, VHS tapes, CDs, and Blu-ray, USB-sticks, SSD
digital copies are always completely identical to the original
error-detection and -correction codes exist for digital data
most of the data we encounter has some redundancy
uniform areas in pictures, silence in sound, values that are changing in a very predictable way
compression (data redundancy removal) is much easier with mathematical algorithms that work with discrete values
digital representation summary:
easier to process digital data
easier to transmit reliably
digital signals can be completely regenerated (if the distortions are not too severe)
easier storage and compression