We explain what the binary system is, how it works, its applications and other characteristics. Also, solved exercises.
What is the binary system?
The binary system or dyadic system It is a fundamental numbering system in computing and information technology in which all numbers can be represented using figures composed of combinations of two single digits.
In the case of binary code, the digits used are zeros (0) and ones (1). We should not confuse the system with the code, since the former could operate with digits such as a and b (since the logic is the same), while the latter operates specifically with 1 and 0.
The binary code is fundamental for the construction of the computers that we know today, especially because it adapts well to the presence or absence of electrical voltages, thus giving rise to a bit of information: present or absent, that is, 1 or 0 , respectively.
However, binary code was not invented exclusively for the world of computing. Already in Eastern antiquity, many mathematicians such as the Hindu Pingala (c. 3rd or 4th century BC) had proposed it, coinciding in many cases with the invention of the number 0.
In fact, oracular books such as the I Ching are composed based on their own code, ordering their hexagrams in series equivalent to 3 “bits”. Later, the Chinese philosopher Shao Yong (1011-1077) arranged them according to a binary method.
For its part, The modern binary system was the work of the German philosopher Gottfried W. Leibniz (1646-1716). Later, in 1854, the British mathematician George Boole (1815-1864) detailed Boolean Algebra, fundamental in the development of the current binary system in electronic circuits.
The first attempts to put this system into practice were the work of the Americans Claude Shannon (1916-2001) and George Stibitz (1904-1995) in 1937.
See also: Programming
How does the binary system work?
The binary system It works based on the representation of any information using two figures. In the binary code they are 0 and 1, but they could well be any, as long as they are the same and represent the same thing: a binary opposition, such as yes or no, up or down, on or off.
In this way, this code allows information to be “written” using similar physical elements: the polarity of a magnetic disk (positive or negative), the presence or absence of electrical voltage, etc.
Therefore, the binary system allows you to “translate” any letter or decimal value into a binary sequence, and even allows you to perform arithmetic and other types of operations.
For example, the letter A in the binary code is represented 1010, while the number 1 is represented 0001. In other codes, that same information could be represented binary as abab and bbbaeither +**+* and ***+ For example.
In this way, according to the binary code, the word etcetera would be represented like this:
01100101 (e)
01110100
01100011 (c)
11000011 (e)
10101001 (´)
01110100
01100101 (e)
01110010 (r)
01100001 (a)
Characteristics of the binary system
The binary system is characterized by the following:
- Use any two units (1 and 0 in the case of binary code) to represent specific information through specific sequences of said digits. There must always be two, with completely distinguishable and mutually exclusive values (there cannot be 1 and 0 at the same time).
- Represents the basis of computer and computing systems in which a sequence of eight bits constitutes a byte of information, corresponding to a letter, number or character.
- Allows you to translate any data expressed in decimal, hexadecimal or octal notation, among other information notation systems (ASCII, etc.).
- Allows reading of real conditions and materials whose physical states can be one or the other: magnetic polarity, voltage, etc.
Applications of the binary system
The binary system allows numerous current uses, for example:
- Programming of microprocessors.
- Encryption of confidential information.
- Transfer data from one computer system to another.
- Communication protocols digital computing.
Solved binary code exercises
Convert from decimal system to binary system:
23 = 10111
17 = 10001
20 = 10100
Convert from binary system to decimal system:
1111 = 15
10110 = 22
10000 = 16
Continue with: Computer file
References
- “Binary system” on Wikipedia.
- “What is the binary system” (video) in UnProfesor.
- “Numbering systems: binary, octal and hexadecimal” in the National Institute of Educational Technologies and Teacher Training of the Ministry of Education of Spain.
- “Binary Code” in IONOS Digital Guide.
- “Binary code” in The Encyclopaedia Britannica.
