Humans have grown counting from one to 10, in a decimal system, and yet we all know that today’s PCs work in a binary system , but do you know why this is so? Why isn’t the decimal or even the hexadecimal system used instead? In this article we explain everything.
All the main numbering systems we use are “positional” , in the sense that the value of the number is determined by where it is placed. We call this the place value (units, tens, hundreds …) and it helps to determine the magnitude of the number. For example, the decimal system that we are all most familiar with indicates how much a “2” is worth for the position it is in, since 2 is not the same as 20 as it is 200.
The value of numbers
But this has not always been the case. This way of representing values is relatively modern, and requires the use of zeros as placeholders. This is why older number systems like Roman numerals or Egyptian hieroglyphs do not use this place value, but add all digits to get the total value.
Using this basic place value concept, we have created different numbering systems or ways to write numbers. These are named for the number of increments per place, that is, how many times can you increase the value of a single place before you have to “move” it to the next. For example, on a decimal basis we can increment the place of units nine times with 10 different digits (counting zero) before going from units to tens.
Why PCs use binary system
When we were children, we were taught to count on our fingers: ten fingers, ten numbers. To count more than ten, you kept a finger closed while you counted the others, and this is the base 10 or decimal system, the system we use every day for practically everything.
However, PCs cannot use base 10, since the hardware we would need for it would be terribly complex . For this reason, PCs use the binary system (or base two) that only has two values (ones and zeros) to count, since, as you know, processors are made with transistors inside that are nothing more than small switches that let pass or they do not let electricity pass, thereby representing the ones and zeros respectively.
In other words, PCs are not capable of counting in decimal or hexadecimal, since their circuits can only represent two states: on and off, ON and OFF, ones and zeros. Therefore, the most natural thing is that its “language” is binary, composed of ones and zeros, and literally every bit of data that a PC manages is nothing but a string of ones and zeros.
Many will say that PCs also manage data in a hexadecimal system, and it really is a case that is a bit on the edge. It is used as a means of representing binary values for humans to understand: a single place value in hexadecimal represents four bits of memory, two places are eight bits, or one byte.
That is why you will see that hexadecimal is used to represent the value of memory registers , since it is easier to read than large strings of ones and zeros, but at the bottom they are still binary data.
Certainly, it would be most convenient if we could use a unified numbering system for everything, but unfortunately each numbering system has its own purpose, so we are condemned to use more than one and in the case of computers, this is the binary .
