Numerical systems

 Numerical systems What is it? A numbering system is a set of symbols and generation rules that allow to build all valid numbers.  These rules are different, for each numbering system considered, but a rule common to all is that to build valid numbers in a numbering system determined (decimal) only symbols allowed in that system can be used.

 Decimal system The decimal system is a positional numbering system in that quantities have a base 10 and can be represented with a different number and consists of 10 digits: One (1), Two (2), Three (3), Four (4), Five (5), Six (6), Seven (7), Eight (8), Nine (9) The decimal system is used everywhere and is the base for the other number systems, such as binary, hexadecimal, and octal.

 Octal system What is it: Octal system. The number system in base 8 is called octal and uses the digits 0 to 7. Octal numbers can be constructed from binary numbers by grouping every three consecutive digits of the latter (from right to left) and obtaining their decimal value. How to tell: The largest octal digit is 7; in this way, when counting in this system, a digit position is increased from 0 to 7. When 7 is reached, it is recycled to 0 for the next count; in this way the next digit position is increased. For example, to count sequences, in the octal system it will be: • 0, 1, 2, 3, 4, 5, 6, 7, 10. • 53, 54, 55, 56, 57, 60. • 375, 376, 377, 400.

 Hexadecimal system The hexadecimal system is a method of positional numbering that uses the number 16 (Base-16) as a base, that is, there are 16 possible digit symbols. Their numbers are represented by the first 10 digits of the decimal numbering: 0,1,2,3,4,5,67,8,9; and the interval from number 10 to number 15 is represented by the letters of the alphabet: A, B, C, D, E and F. The hexadecimal code to be able to read it easier uses decimal numbers for all the characters and for that it uses the ASCII code: Use of that sistem: The use that is given today to the hexadecimal system is directly linked to the branch of computer science and communication sciences in which the CPU uses the byte or octet, as the basic unit of memory. This system is also used in programming although computers do not run in hexadecimal, but programmers use it to represent binary addresses in a human-readable format when writing code. This is because two digits of hexadecimal can represent a full byte, eight...

 Binary system Binaries are a base 2 number system. Base 2 means that there are only two digits, 1 and 0, that correspond to the on and off states that the computer can understand. A single binary digit (such as "0" or "1") is called a "bit." For example 11010 is five bits long. In binaries, the first digit is 1 in decimal. The second digit is worth 2, the third is worth 4, the fourth is worth 8, and so on, doubling each time. Adding all of this gives you the number in decimal. So: 1111 (in binary) = 8 + 4 + 2 + 1 = 15 (in decimal) Bits: A single binary digit (such as "0" or "1") is called a "bit". For example 11010 is five bits long. The word bit comes from the English words "binary digit" How to identify them: To show that a number is binary, we put a small 2 behind it: 101 2 This way nobody will think that it is the decimal number "101" (one hundred and one). The use of this numbering system is usually i...