Analog VS Digital Data

What is information

• Information: some knowledge you want to record or transmit 

E.g., person’s weight, current time, picture of a cat

What is Data

• Data: the representation of the above 

• Person’s weight: 63 kg, 139 lb, 9 st 13 (“9 stone 13”) 

                             One average goat, or seven watermelons 

Time: 13:34:16, 1:34:16 PM, 18:34:16 UTC, 183416Z

What is Signal

• Signal: some means to record or transmit data or information 

• Voltage, current, handwritten note, markings on wood (Not a major focus of this course)

Types of Information (infinite)

• Inherently continuous (with infinitely many values in any range) 

• Mass 

• Temperature 

• most other physical quantities (e.g., body temperature, blood pressure) • Sound, images, video

Types of Information (Not Continuous)

• 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

What is Analog and Digital Data

• 2 main ways to represent information 

• 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

Examples:

• Analog Data: spirit (or mercury) thermometer exemplifies analog information display where the liquid level continually rises and falls in direct proportion to the temperature 

• Digital Data: digital displays only show (represent) information in a discrete fashion

What is the current temperature?

• the thermometer on the right provides infinite precision, directly corresponding to the actual temperature 

• our reading is limited only by our ability to measure its value

Are computers Finite or infinite?

• Information often possesses an infinite range of values 

• E.g., how many real numbers are in the interval [0..1]? 

• However computers are finite and also deterministic (i.e., 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 an 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: 

• digitization of video: 24–30 still frames per second 

• dividing a still picture into pixels (e.g., HDTV: 19201080) 

• digitization of audio 

2. Quantization (truncation) converts an infinite range of values to a finite one examples: 

• 1/3 = 0.33333 ( some finite number of digits) 

• Pi = 3.14159 

• √2 = 1.41421

•  RGB colour range per pixel (discussed later)

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

But… the information can be lost???  

• YES, some information is allowed to be lost 

• BUT 

• We decide what can be lost at the very beginning 

• There are many mechanisms to determine proper parameters to digitise analog data (continuous information) with as much precision as necessary

• Nyquist–Shannon sampling theorem (yes, that C. Shannon)

• Quantization error models

• Any losses are completely avoidable after the digitization is performed

Bits 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 

• E.g., “Mb” for megabit and “MB” for megabyte

Binary vs. Decimal Multipliers 

Decimal

• Communication (Gigabit Ethernet: 1 billion bits per second) 

• Data transfer (PC3-12800 RAM transfers 12,800,000,000 bytes per second)

• Clock rates (A 2-GHz CPU receives 2,000,000,000 ticks per second) 

• Storage, by manufacturers (10 TB: 10 trillion bytes) 

• Storage, by some operating systems (macOS, Linux) 

• DVDs 

  Binary 

• Memory Capacity (8 GB: 8,589,934,592 bytes) 

• Storage, by some operating systems (Windows, occasionally Linux; 3.63 TB: 4,000,000,000,000 bytes) 

• CDs

So, why digital? Why binary?

• Computers cannot work well with analog data 

• Discretize the data (i.e., 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 a 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 effects (e.g. in the transmission medium) 

• similar effects at play when the signals are recorded

Benefits in signal transmission (2)

• Analog: degradation of analog signals is permanent; there is no way to determine if the distortion was not present originally 

• Digital: 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(
the state of being not or no longer needed or useful)

• 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 (separate) values

Digital Representation: Summary