The numbering systems are the form of representation that we count on to represent the mathematical values that we find in the different mathematical operations that we have at our disposal. Some of the most common are the decimal system and the binary system, which have notable differences as we will see later.
While one of them only has two digits to represent all the possible combinations of values, the decimal system has up to nine different options that can be included when we perform operations and want to express mathematical options. Therefore, the understanding of the operation of each of the systems and their subsequent practical application is of enormous importance.
What is the Binary system and the decimal system?
Therefore, before explaining the procedure on how to go from one system to another, it is necessary to know in depth what both the binary system and the decimal system consist of. Binary is still considered today the main numbering system in all fields of computing and electronics. Use only the zeros and ones to express the different possibilities that can be used to combine. In fact, surely you have heard of the word bit. Well, the bits are nothing more than simple representations of the binary system.
The origin of the binary system is really distant. In fact, it is considered one of the first number systems in the history of mathematics. It arose in ancient India through a mathematician and has been updated ever since. Since then, the ancient Chinese civilization in the East, as well as the Greeks and Romans until reaching one of the main historical figures such as Leibniz, were in charge of perfecting this type of system.
Although his role was played in the 17th century, this scholar is even considered several centuries ago as the founding father of this number system. Even, it must be taken into account that the bits mentioned above are contemporary with his participation De él. However, the one who laid much of the foundation for this system was this philosopher, mathematician, and scholar of French origin who laid the modern cornerstone for the advancement of this type of system.
On the other hand, the decimal system can be considered as a complement to the binary system. Although it has many more values than its predecessor, the reality is that this number system is on horseback. As we have said, the binary system is based on the combination of values that are between zero and one. The decimal, on the other hand, performs the same function but with the main variable that the values extend from zero to nine. Therefore, it has more than triple the possibilities that combining them reach up to a thousand and one combinations.
Benefits of knowing the Binary system and the Decimal system
However, there are numerous advantages of knowing both the binary and decimal systems, and of being able to go from one system to another operating correctly, since it has numerous applications in the field of electronics. The most prominent are:
- Living history of mathematics. As we have seen previously, the binary system is one of the first numbering systems to exist, and one with the longest history. Therefore, its understanding is absolutely necessary for anyone who wants to be a scholar of mathematics.
- Develop a professional career. Working as a computer scientist or developing careers related to telecommunications or electronics require knowledge of the binary system and the decimal system. Therefore, these requirements will be taken into account for any type of job position with these characteristics.
- To study math. If you want to study mathematics at the University and you don’t want to stress yourself too much, it will be necessary to have a good foundation, which involves knowing the binary system and the decimal system adequately.
- Improve our calculation intelligence. Constantly going from the binary system to the decimal system without the use of technology requires great calculus skills. Therefore, a constant practice of this type of operations will help a lot to develop our options at the calculation level.
Therefore, if you are one of those who is passionate about mathematics, you are interested in learning the concepts of binary and decimal systems, as well as delving into them and learning to operate correctly with all of them. In this way, you will obtain these main advantages, in addition to many other qualities that must be taken into account for the future.
How to convert a Decimal number to Binary?
For this reason, once the two systems have been presented, the next step is to find out what are the steps to follow to go from a decimal system to a binary system without any kind of setback and effectively. We are going to explain it in a didactic way so that you can easily understand it, while you are putting it into practice at the same time that you are reading it. After knowing how to go from a binary number to a decimal, to begin with you must place the combination of decimal numbers in a distributed and ordered way since confusing any of the terms can end up resulting in an error that ends the transformation. In this sense, we recommend you to put them in line with spaces to be able to work with them.
Once you have raised the system, the first operation that we must carry out is to divide each of the components of the system by two. In this sense, if the result of said division comes out as even, we will put a zero in its place. On the other hand, if, on the contrary, the result is an odd number, we will place a one in its place. In this way, we have already gone from a combination of up to nine different possibilities to another that differs between only one and zero. However, do not forget that there are infinite combinations between numbers between one and nine. Therefore, the ones and zeros must be placed when the name in question is already indivisible. Take for example the number 78.
What we must do in this case is divide the name by two continuously until it can no longer be divided. When we obtain a prime number is when we must decide if it is an even number or an odd number, and therefore, assign it the value of zero or one. We are going to carry out a practical example so that it is understood how it is possible to go from a decimal number to a binary number in a continuous way. To do this, we start from the base number 79. As we can see, it is odd. Therefore, the first number of the sequence will be a one. Now we proceed to divide this number by two, always rounding.
Dividing by two successively gives the binary number
Dividing by two would give us 39, if we rounded up. This is another odd number. Therefore, the next number that we will apply in the rule will be another one. We divide it by two again and the result is 19. In this sense, another one is applied again. We divide 19 by two again and the result is 9, which is also odd and, therefore, another one is applied again. In this case, we will have the first even number of the sequence. 9 between two can never be five since it would be ten. Therefore, it is necessary to place a 4, which, being even, a zero is applied to it.
The four divided by two gives two exactly, and being even, another zero is placed again. In this case, the two is divided by itself and the result is one, which is an odd number. Since we can no longer obtain more divisions, we conclude the operation and we can now express the final result that consists of putting all these numbers that we have been obtaining in order. Therefore, we can conclude that the binary number of the decimal 79 is 1111001.
Basically, it consists of performing the opposite operation to when we go from a binary number to a decimal number. In the mathematical world we find multiple cases in which opposite operations can be performed. In addition to the addition and subtraction of natural numbers, which seems obvious, when we advance in mathematical knowledge we will find derivatives. The opposite of a derivative would be an integral. It also happens with matrices and logarithms. The fact of being able to carry out these opposite operations is also a good system to control if we have done our work correctly.
Therefore, mastering both the operation to go from a binary to a decimal system and vice versa is essential to understand much of the history of mathematics. Not only that, since we also put into practice basic knowledge such as divisions, coordination and the need to configure values. In this sense, in addition to the benefits mentioned above, you should not forget that knowing how to go from a binary system to a decimal system and vice versa is absolutely recommended for your understanding and progress.