24/september/2019 


Notes 

This date we begin the fourth period, what nerves!
From now on the whole blog will be in English and to start we have a task: what are digital systems?, numerical systems... and etc.


What is a numerical system?


Basically it is the set of symbols and rules that are used to represent numerical data or quantities




BINARY NUMBERING SYSTEM.

This base 2 system is the easiest of all to have only two digits,
was introduced by Leibniz in the 17th century, it is the system that they use internally the digital circuits that configure the hardware of current computers.  The two digits, called bits (Binary Digit Contraction), are the one (1) and the
zero (0), so the decimal equivalent will be obtained by adding the weights corresponding to bits 1.

In most significant bit (MSB) is the one that is located more to the left (the one with the highest value). The least significant bit (LSB) is the one that is more to the right and has the lowest value. For the measurement of information units represented in binary, a series of bit multiples that have their own name are used:


  1. Nibble or Quartet: It is the set of four bits (1001). 
  2. Byte or Octet: It is the set of eight bits (10101010). 
  3. Kilobyte (Kb): It is the set of 2 ^ 10 bits (1,024 * 8 bits) 
  4. Megabyte (Mb): It is the set of 2 ^ 20 Kilobytes bits (1.0242 * 8 bits)
  5. Gigabyte (Gb): It is the set of 2 ^ 30 Megabytes bits (1.0243 * 8 bits) ƒ
  6. Terabyte (Tb): It is the set of 2 ^ 40 Gigabytes bits (1.0244 * 8 bits)

 The reason why the factor 1,024 is used instead of 1,000, is because it is the multiple of 2 closest to 1000, an important issue from a computer point of view (210 = 1,024)

OCTAL NUMBERING SYSTEM. 


It is a numbering system in base 8 that uses 8 symbols to represent quantities. The symbols used are: 0, 1, 2, 3, 4, 5, 6, 7. This system is also positional, since each of its figures has the position relative to the decimal point which, if it does not appear, assumes implicit on the right side of the number, it provides a convenient method for representing binary codes and numbers used in digital systems.



HEXADECIMAL NUMBERING SYSTEM.


The hexadecimal system uses base 16. Thus, it has 16 possible digital symbols. Use the digits 0 through 9, plus the letters A, B, C, D, E and F as your 16 digital symbols. Each hexadecimal digit represents a group of four binary digits. It is important to remember that the hex digits (Hexadecimal Abbreviation) from A to F are equivalent to the decimal values ​​of 10 to 15.

(bibliography)


Conversion from Binary to Octal.


To convert a binary number to octal, an inverse process is performed
previous. The 3-in-3 digits are grouped from the decimal point to the
left and right, replacing each trio of binary digits with its
equivalent octal digit.




Binary to Hexadecimal conversion.


A reverse process is performed to the previous one. Binary digits are grouped
4 in 4 from the decimal point to the left and right,
replacing each quartet with its corresponding hexadecimal digit.
Adding zeros when necessary to complete a 4-bit group.


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