All those interested in data and Information Technology have surely heard of what is known as a binary system. This system is formed by two values represented as one and zero. Therefore, an infinite combination of these values can be achieved. This system served to launch numerous devices related to the telecommunications sector.
However, over time the well-known decimal system was put into operation, which has many more values than the binary system. In this sense, instead of staying only with one and zero, the decimal system extends to nine. For this reason, we can express combinations of numbers that go from one to nine, passing through two, three, four, five, six, seven and eight.
What is the Binary system and the Decimal system?
The Binary system and the Decimal system make up two of the main numbering systems that we can find in the mathematical world, and that are applied in numerous sectors. In this sense, we can define a numeral system as the set of finite values that serve to express the different numbers that we can represent on a line. In addition to the two main ones, Roman and hexadecimal are also some that are used today, although in a minority. However, between the Binary system and the Decimal system there are numerous differences that must be known before proceeding to explain how to convert a binary number to a decimal in an appropriate way .
One of the main applications of the binary system is in the field of computing. In this sense, if one of your objectives is to work as a computer scientist, you should know this system inside out. Therefore, this article may be of interest to you. As we have said before, this type of system only uses two digits, composed between one and zero. Therefore, a possible combination in this system is 110010101001, without going any further. In addition, in the field of computing and electronics, this system is called bits. The origin of this system, although it may seem really close, is totally distant. In fact, it was a mathematician from ancient India who started this very system.
The evolution of this system was carried out progressively throughout history passing through ancient China until reaching the scholar Leibniz, who in the 17th century made an advance in the binary system that has led it to be considered today as the father of this system. Obviously, different advances were carried out at the same time until we reached the well- known bit system that we currently have and that is used so many times in the day-to-day life of many professionals related to telecommunications.
Instead, the decimal system can be considered complementary to the binary system. It has exactly the same structure but with many more values and possibilities. If in the binary system only two possible values such as one and zero are recognized, in the decimal system all these values can range from one to nine. Therefore, the possible combinations of numbers between one system and another are completely antagonistic and much more numerous in the latter case. In this sense, it is necessary to understand what each of the systems offers us to carry out the operation correctly.
Benefits of converting a Binary number to a Decimal
All in all, there are numerous benefits offered by both the binary system and the decimal system and the operation that helps us to go from one type of system to another. In this sense, the most outstanding that we can find are the following:
- Know part of the history of mathematics. The binary system is part of the living history of the mathematical world, emerging before Christ and extending its advances until practically today.
- Develop a career in the world of telecommunications. The applications in the field of telecommunications are totally direct when we talk about the binary system. Therefore, it is necessary to understand it in order to develop a successful career in this field.
- Know how to move from one system to another. In addition, in many situations in our working life it will be necessary to go from a binary system to a decimal system effectively. Therefore, if we do not know how to do it, our qualities will be reduced.
- Improve our intelligence at the calculation level. In addition, many calculus skills are required to correctly understand the possible interpretations that both the binary system and the decimal system offer us in many mathematical aspects.
How to convert from Binary number to Decimal?
Thus, once both the binary system and the decimal system have been presented, we will proceed to explain the steps that must be followed in detail to go from an initial binary number to a decimal number appropriately, and without making any mistakes. that can penalize us in our operation and make us start over from scratch. Every binary number will have a power next to each value. Let’s take the example of 10011011 raised to two. The first step that we must carry out is to represent this series of values by putting the exponent the number of times that we have a binary number. From left to right, if we have seven numbers, the number on the left will rise to seven and we will go down progressively until we reach zero..
In this sense, we will start with a number raised to seven and end with a two raised to zero. We will carry out the calculation of the powers and we will express the result in the same way that we had represented the series of binary numbers. In this sense, the result would be: 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1. Once we have the results of the powers properly written, we must return to the previous binary numbers and write, in the same order of the results of the powers, each of the values of the binary system that we have at our disposal.
So that you don’t get confused and express the values properly, it is recommended that you draw a series of lines that connect each of the values and thus manage to correctly relate the different values that you have at your disposal. It is important to carry out this step since in this way you avoid having to make any type of mistake by confusing rows that ultimately hinder the final result of the operation that you are going to end up carrying out. Once you have placed each of the results in line you must relate them to the binary digits. In this sense, if, for example, 128 has a number 1 as a binary component, it will be necessary for this one to be placed at the bottom and so on until reaching the complete series .
The importance of not making mistakes when placing the numbers
It is important not to make any mistakes when relating binary numbers to powers as the next step requires great precision to get it right. Do you remember that each of the numbers was between one and zero? It is done because when passing it to the decimal system, the numbers that correspond to a zero will not be added while those that correspond to a one will be included in the sum. In this sense, if we take the previous example we should take 128, 16, 8, 2 and 1 getting a total result of 155. This is the decimal result.
However, before completing the operation it will be necessary to express it correctly. As it is a series of ten numbers, the exact result is 155 with a ten below that indicates the final number of numbers that are expressed in the binary code, which, as we have explained previously, is made up of up to ten different numbers. This is the traditional method but, obviously, there is another much faster one that requires having deeply internalized the entire binary system and the need to quickly apply the powers. Otherwise, making a mistake is really easy. For this reason, we are not going to explain this method in depth since the first one is simpler and easier to understand about how to go from a binary number to a decimal number without problems.
Obviously, technology can also be at our service, since numerous applications and platforms can be found on the Internet that can be used to demonstrate in a really simple way how to go from a binary system to a decimal system without any type of problem or setback that may hinder our operations. In this sense, today we have many options available to achieve our purpose of going from a binary system type to a decimal one without any difficulty. Therefore, you just have to choose the one you like the most and carry it out.