Representation of data

 Representing letters, symbols -

Often wondered how the text, symbols are interpreted by the computer ?

The text and symbols are interpreted by the computer using binary digits. Texts and symbols are represented in string of bits. the size of string is of 8 bits where 0  is kept at the Most Significant Bit (MSB).

Such representation was formulated by American Standard Code for Information Interchange (ASCII).The binary form of text and symbols are called as ASCII values. ASCII values acts as a translation between the binary form and the final presentation. However, later many different language came for representation but the size of the string was insufficient as the max size was only of 8 bit.

Additional bits for ease of conversion of other language scripts was added. It has been increased from 8 to 24-32 bits. In 24-32 bits it left space for many symbols and scripts of language that can be added. This work was done by Unicode Transformation Format(UTF). 

Image courtesy - https://www.pinterest.com/pin/735705289121827835/

Q]What is the major difference between the upper-case letter ASCII and lower-case letter ASCII ?

 ->The difference in the ASCII values of upper-case and lower-case letter is the same binary from 6 bit to 7 bit out of the total 8 bits in the lower-case letters and upper-case letters.

       

     example :-  A  -  0 1 0 0 0 0 0 1                    a - 0 1 1 0 0 0 0 1                              

                                        8 7 6 5 4 3 2 1                         8 7 6 5 4 3 2 1

                     

                      upper case has constant (1 0) in 6-7 bit.

                      lower case has constant (1 1) in 6-7 bit.

Representing Numbers - 

Numbers in computer system can be represented using ASCII values but the ASCII values have the limit of storing and displaying only 127 decimal. since ASCII value uses 8-bit to present text and other symbols.

Therefore a different type of notation consisting of 0's and 1's is used. This notation is called as binary notation.

Lets understand binary notation through the analogy of odometer :- 

Odometer - An odometer is a device used in the car that calculates the distance travelled by the car. Lets suppose the odometer has the size of 4 rotational relays/disks/reel.

As soon as the highest digit rotates in the first reel, the reel adjacent to it also rotates else the digit in the adjacent reel remains same.

Similarly the binary notation uses this logic and rotates 0's and 1's with 1 being the highest digit. As the 1 rotates to 0, the adjacent bit also changes else it remains the same. Thus the following pattern is created. 

binary notation          number

0000                                 0

0001                                 1

0010                                 2

0011                                 3 

0100                                 4

0101                                 5

0110                                 6

0111                                 7

Representing Images - 

Images in computers are represented through a large collection of dots, each dots is called as a pixel. The orientation of each pixel is encoded in binary format. The large representation of each 'encoded' pixel is called as a bit map.

Such format of representation of image is very convenient to decode for facsimile machine that uses only black and white images whose bit value can be considered as 0 and 1.

For more color based application more complex technique of encoding pixel into R-G-B is used where each pixel has RGB value encoded. In RGB encoding 1 byte is required to represent the intensity of each pixel and 3 bytes are required to store each pixel.

More elaborative form of RGB encoding uses luminance and chrominance as its two components to represent the image. Luminance is the amount of red green and blue light present in the pixel, whereas blue chrominance and red chrominance is luminance minus the amount of blue/red light depending on the chrominance.

The popularity of RGB encoding in luminance and chrominance was used in television broadcast because it made it compatible of same image to be represented in black and white television using grey-scale. Luminance without the chrominance gives black and white image which avoided multiple format of images for different monitors.

Example of how an image is represented using bitmap and converted to color using grey-scaling, luminance and chrominance 

Image courtesy - https://www.researchgate.net/figure/Digital-image-representation-A-Logical-image-with-values-1-for-white-and-0-for_fig2_344785470 

Image representation using bit-map produces issues in scaling where the pixels appear uneven and images appear to be tearing when the image is made to zoom. Therefore in modern systems geometric algorithms is used to produce images in lines and curves. The Font system that we use today was developed by Apple and Microsoft as TrueType. Further for more general pictorial data a system developed by Adobe called 'PostScript' is used. The geometric means of representing images is also popular in Computer-Aided-Design (CAD) systems in which in which drawings of three dimensional objects are displayed and manipulated on display screen. Basically CAD is software commonly used by Architects, graphics designers and certain engineers to create 3-D models in order to achieve specific purpose like understanding real-simulation of object with its surrounding.

Representing Sound - 

Sound in computer system is represented using a series of amplitude. Amplitude refers to the distance travelled by a sound wave. Ranges of amplitude like 0,0.5,2,1.5,2,3,4,3,0 where 0 to 2 would represent rise in the amplitude and pitch and 2 to 1.5 would represent the fall in amplitude, this goes on consequently until the sound is stopped.

Sound is encoded in the series of the amplitude for every 8000th of a second. Later this sound is decoded from the other receiving end. Although 8000 sound sample per second may seem very large but it is not recommended for high fidelity audio, we will understand that in a bit below this part.

For better fidelity , Musical Instrument Digital Interface (MIDI) is used in industries like video games, movies, music, electronic keyboards where the sound is rather later interpreted than encoded. This solves large storing problem. It generally samples audio at 44100 samples per second.

Coming back at the storage part, by using amplitude series encoding it would take 2 million bits at the rate of 44,100 samples per second which on conversion turns out to be 0.25 MB. Although not significant but compounding the audio more and more makes this size a very large size.