Analog vs. Digital Information

information

some knowledge you want to record or transmit

• ex. person’s weight, current time, picture of a cat

data

the representation of the above

• person’s weight

  • 63kg, 139 lb…

  • 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:

1. Analog data

2. 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

1. sampling (discretization)

   • converts continuous variation to discrete snapshots

   • examples: digitalization of video; dividing still picture into pixels; digitalization of audio

2. 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

  • Nyquist—Shannon 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. ‘Mb’ for megabit and ‘MB’ 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 ‘noise’ 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