May 27, 2023

What are subnormal numbers and why are they important in a computer?

For there to be subnormal numbers, there must first be normal numbers, right? Well, let’s see what this is due to, but we already anticipate that the reason for all this is computers.

In computing, subnormal numbers are numbers that fill the underflow gap in the vicinity of zero in floating-point arithmetic. Any nonzero number with a magnitude less than the smallest normal number is subnormal.

This is due to the need for a computer, all those decimal places that we find in computing and how difficult they are to handle. Because somehow you have to encode the numbers in the computers.

The system that orders these numbers is called a floating point, and the first person to propose it was the Spanish Leonardo Torres Quevedo (1852-1936), who was a civil engineer, mathematician and inventor.

Computers, as they encode everything with zeros and ones, specifically integers are written with their binary expression. With 8 bits, for example, the number 6 is written: 0000 1010. But then how do we write numbers like 75,56?

Here comes the topic of floating point. The first thing we must do is choose how many bits we are going to use to represent each number, being the usual or 32 bits or 64 bits (surely this sounds like you) although you can use more in case you need more precision.

All this operation follows standards so that computer manufacturers and programmers can work in the same way and thus understand each other between components, operating systems and programs.

And is that the purpose of having subnormal numbers is to smooth the gap between the smallest normal number and zero, since otherwise it would be very difficult for computer equipment to be precise.

With all this operation we make sure that we do not lose the precision of normal numbers and that between the smallest normal number and zero we have many more tiny numbers that lead to many rounding and division problems.

From the components that a computer must have, through the principles of programming, to the invention of web pages, we are going to review some of the names that traced the course of the history of computing.

Although this precision between subnormal numbers is not infinite, and there is a time when numbers are missing, hence there are 64-bit systems instead of 32, and other more specialized techniques.

And rest assured, if you have not understood anything our friends from Derivando, the YouTube channel that we have left you, explain it even better. And if you still don’t understand it, calm down, your computer handles subnormal numbers perfectly.