El binary system It is of great importance in the computer area, since they make possible the interpretation of information and numerical values by the various technologies, which will be detailed in this information.
Numerical representation in computing for the operation of technologies
What is a binary system?
It is a numbering format that is used in computing so that the operation of a computer is carried out, they only make use of two numbers, zero and one, being the necessary ones to be able to represent the information in general, which is of great importance because the operation of these devices is performed only in two levels of voltage, current and more, appearing according to the number of numbers used.
History
The first presentation of the binary system It was made by a mathematician many years ago, close to the times of the third century, very close to the discovery of the number zero, which was of great importance to start this development; other important aspects in the story was by I Ching who made a series that consisted of three bits and six-bit binary numbers, which have been used to make binary combinations.
There were binary-type arrangements from the 1605th century, made by Shao Yong who presented an order from this realization, characteristic for having a sequence from zero to sixty-three, exhibiting how the generation strategy of this process was, as As the years passed, points of greater importance to the subject were highlighted, in the year XNUMX Bacon Francis provided an explanation on how the letters could be presented in binary numbers.
Publications of books were made that were emphasized by providing a description of the binary system, documentaries were also made where different types of symbols were applied, both Chinese and mathematical, using exactly 0 and 1 as shown today, then by the year 1854 the publication of an information was made by George Boole, where he explained a logical system called Boolean Algebra.
This system was established as a point of great importance in the development of electronic type circuits, it contributed a large part of this type of work, so it was essential to know about the binary system and the different points that were related.
The binary representation has been presented as a great participant in the development of this area, if you are more interested in it we recommend reading about the evolution of computing.
Applications
Each of the important aspects of this topic were applied for different purposes by the professionals who were dedicated to it, among them Claude Shannon is named, who presented his thesis applying Boola's Algebra as well as binary arithmetic, being of great importance because it was the first time that switches and relays were used, years later Stibitz George made the construction of a calculator using relays.
In 1940, improvements were presented for the creation of calculators, exhibiting those that used complex numbers, which were demonstrated by exhibiting their effectiveness, as more work was done on it, different types of commands were transferred to the calculator, through the use of a phone line.
Currently the binary system is used for various purposes, since it is based on a specific operation in technology, today the advance has been exhibited in a great way, therefore, its relevance has been constantly presented, among one of the most Highlights is the programming of the microprocessors, being of great use in computing.
Other applications have been the encryption of information, for those that require high privacy, since they are confidential, the use of the binary system has been effective, being able to transfer different data in varieties of systems has been an advantage for the times. current, as well as it is directly related to the application of protocols so that there is communication in a digital way.
The binary system is presented in the development and advancement of technology, as what is currently observed, we recommend that you read about examples of digital technology.
Representation
As previously highlighted in the binary system, only 0 and 1 are used, they are two figures that are represented by other digits, such as bits, since they show the specific context for the correct interpretation of it, detailing the following examples to understand each sequence:
The assignment of symbols will be of great importance, in a computer each of the numbers that are found is found by some type of voltage, this can also be related to other types of points such as polarities, magnetism, but everything will depend on the symbols that are used, it is not so easily visualized, for this reason the representation is essential and the Arabic numerical values are normally used.
Generally 0 and 1 are used, but other types of representations can also be carried out, since it has certain variations, therefore, it is necessary that the following points be taken into account:
- 100101 binary, this is a commonly used format.
- 100101b, this is another representation to indicate a type of binary format.
- 100101B, it is presented the same as the previous case.
- Bin 100101, is a prefix used for the binary type format.
Conversion
One of the points that should be highlighted are the conversions that are made between binaries and decimals, there are various cases, which differ in certain aspects, therefore, every detail must be taken into account so that the applied process is appropriate and is not complicated to perform, the following are indicated.
Decimal to binary
First, the decimal number value is taken into account, which must be divided by two, the result must also be divided by two, and this process will be applied until obtaining a number that is less than two, to make it easier to understand, it will be highlighted a simple example, so that you can see each of the steps that must be fulfilled so that this simple method can be fulfilled.
- You get the binary number 131.
- Dividing 131 by two gives the result 65 with a remainder of 1.
- Then the division by two is continued and the number 32 is obtained, again with a remainder of 1.
- It continues with 32 that when dividing by two is 16, presenting a remainder of 0.
- Then 16 between two gives 8, with a remainder of 0.
- Eight divided by two is four, and the remainder obtained is 0.
- 4 divided by two results in two, which means that the remainder is 0.
- And two between two is one, therefore the remainder is 0, to finish this process, the last quotient is taken into account that it is one, this is necessary to be able to establish the order correctly.
- A regressive order is established, from the last remainder to the first, which means that the binary system of 131 is 10000011.
It is a very easy method to apply, each of the accounts must be carried out correctly so that the analysis carried out is not wrong, however, there are also other methods that will allow obtaining these results, but in general this is considered the easiest to apply.
Decimal (with decimals) to binary
This is another of the cases that must be considered for the conversion, if a number is obtained with decimals it is possible to carry out its transformation to a binary number, for this, some points to apply must be considered that will allow it to be carried out in the form correct.
- First of all taking into account the integer part of the decimal number, since this is initially converted, in the case that it is 0 or 1, then in the binary system it will be the same way.
- Then the fractional part is considered, for each of them a multiplication by the number two must be carried out, in the event that the result exceeds the number one then 1 must be placed, since it is a binary value, in the case that is less then 0 should be placed.
- At the end of each of the multiplications then the results obtained as binary values must be ordered according to their obtaining.
It is not a complex method, it is actually considered one of the simplest and fastest, therefore, to avoid confusion, some examples will be highlighted that allow it to be understood more quickly, being the following:
- It has the following decimal number: 0,3125.
- Since the whole number is 0, it is placed in the same way for the binary system and the multiplication continues.
- Multiplying by two gives the value 0,625.
- Now we continue multiplying the value obtained by two and we obtain 0,5.
- Again the same process is fulfilled and a value of 1 is obtained.
- Then according to each of the results obtained, considering if it is greater than 1 or not, the conversion to binary is 0,0101.
Now, a different case will be presented, so that you have an idea of what to do when the integer is not 0 or 1, the following should apply:
- The decimal number to convert is 5,5.
- Since the integer is 5, the conversion to binary must include 101.
- Continue by multiplying the decimal number 0,5 by two, obtaining a result of 1.
- Then the binary number must be placed in order, being 101,1.
It is necessary that the conversions are applied in the correct way, that is, that corresponds to the case, since not all are carried out in the same way, depending on what you want to obtain, certain rules and points that relate to binary values as well as decimals, allowing their conversion to be possible taking into account all the aspects that come from the binary system.
Binary to decimal
Other processes that can be carried out is the conversion of a binary number to a decimal number, this is different from the previous cases, so you must be very careful, but in the same way it is quite simple.
- The binary number must be taken from right to left, in order to apply the multiplication.
- Each of the digits must be multiplied by two and must be raised to the consequent power.
- When obtaining each of the results of the multiplications, these must be added and the number obtained will be taken as a decimal.
Binary to decimal (with binary fractional part)
In this case, the binary number is taken, otherwise, the left side is considered first, also applying multiplication by two, which must be raised to the power that continues in its inverse, after each of these are performed. multiplications then the results must be added, and the number obtained will be the decimal.
Operations
Binary numbers can have different applications either for addition, subtraction, multiplication, quotient, this is not obtained in the same way as with natural numbers for some cases, therefore, it is important to know specifically how operations are performed in the binary system.
Addition
In order to carry out the addition operation in the binary system, it is important to comply with certain rules and follow a protocol that allows the calculation to be carried out correctly, it is considered a very simple method, so it is highlighted that the rules are as follows:
- 0 + 0 = 0.
- 0 + 1 = 1.
- 1 + 0 = 1.
- 1 + 1 = 10.
These are the essential points that must be met for a proper addition operation to be carried out with binary numbers, as long as great care is taken to perform these calculations, the whole operation in general will be done quickly and easily, to still understand more about it, an example will be indicated as the process is.
- As an example, the summation of 0011101 and 1101011 is performed.
- The addition must be carried out from right to left, therefore, the figures are placed one below the other to apply the sum per column.
- Then, complying with the rules, the operation begins, first 1 + 1 = 10, therefore, you must place 0 and carry 1.
- Continue with adding the 1 that is being carried with the 0, where 1 + 0 = 1 and this result is added with the corresponding 1, therefore it is 1 + 1 = 10, the 0 is placed and 1 is taken again.
- Continue with the third column, add the 1 that is carried with the 1 of the first term, being 1 + 1 = 10, then now the 10 + 0 = 10 is applied, as in the previous cases, the 0 is placed and carries 1.
- For the fourth column, first it is 1 + 1 = 10 and then 10 + 1 = 11, the one will be placed and one is taken as well.
- In the next column then it would be 1 + 1 = 10 and then 10 + 0 = 0, the zero is placed and 1 continues to be carried.
- The sixth column begins by adding 1 + 0 = 1 and from there 1 + 1 = 10, the 0 is replaced and 1 is taken.
- For the last column, then 1 + 0 = 1 is added and then 1 + 1 = 10, then last if 10 is placed.
- By completing this procedure to perform the sum, a result of 10001000 is obtained, being very simple to carry out, you always have to be aware of the amounts that are being carried, thus avoiding errors.
Resta
For the subtraction operation, certain rules must also be taken into account, being the following:
- 0-0 0 =.
- 1-0 0 =.
- 1-1 0 =.
- 0-1 = 1 and takes 1.
For this, the example is applied with the following figures, 001100011 and 000011110, in the same way it must be done from right to left, the rules are applied in each of the columns and the result of 001000101 is obtained, in order to reach this result the operation was carried out as follows:
- In the first column it is a 0, coming from 1-0 = 0.
- In the next one, 1-1 = 0 is applied.
- The third subtraction is 0-1 = 1, and in addition to that it takes 1.
- For the fourth column, first it is considered that 1 is being carried, then 1-0 = 1 must be applied, then 1 is being carried for the next, and then 1-1 = 0 is applied, which is the one that must be placed in the result.
- Now in the fifth it is applied in the same way as it was done in the fourth column, obtaining 0 in the result.
- In the next one, 1-1 = 0 is performed and then 0-0 = 0, the 0 must be placed.
- The seventh column is 1-0 = 1.
- Then follows 0-0 = 0.
- And lastly, 0-0 = 0.
- Therefore, doing each of these columns in order results in 001000101.
Multiplication
For the case of the product with binary numbers, no specific rules are presented for this operation as in the case of addition and subtraction, to carry out multiplication the operation must be applied in the same way as it is done with decimal numbers, therefore, in this case there are no changes, no other additional knowledge is required.
Division
The same happens with the quotient of binary numbers, the rules that must be met, the process that must be applied is the same as that carried out in usual divisions with decimal numbers, in the same way as multiplication, there are no changes in the applied operation.
