# Hexadecimal system

The **hexadecimal system** is a type of **positional numbering** system that uses the number **16** as its base . Their numbers are represented by the first 10 digits of the decimal numbering, and the interval that goes from the number 10 to 15 are represented by the following **letters** of the alphabet from A – B – C – D – E and F. The use that of We give it today to the hexadecimal system is closely linked to the branch of **computer science** and computer **science** in which, the different operations of the **CPU** use the **byte** or octet as the basic unit of its memory. As this is a number system with **Base-16**, the hexadecimal numbering system uses sixteen different digits with a combination of numbers ranging from 0 to 15. In other words, there are 16 possible digit symbols.

## What is the hexadecimal system?

This system is a type of **positional ****numbering** that uses the number **sixteen** as a base and in which the numbers they contain are represented by the first ten digits of the decimal numbering, representing the numbers from ten to fifteen with the letters of the alphabet that go from the **a** to **F** .

- What is the hexadecimal system for?
- Hexadecimal system characteristics
- History
- Who Invented the Hexadecimal System
- Hexadecimal System Symbols
- Examples

## What is the hexadecimal system for?

The hexadecimal system is commonly used in **computers ****and digital systems** to reduce large strings of binary numbers into sets of four digits so that we can easily understand them. Its current use is closely linked to **computing** because computers usually use the byte or octet as the basic unit of memory. Hexadecimal notation is also used within **web pages** and in **computer systems** to indicate some values. An excellent example is the color notation used in **HTML** web templates .

## Hexadecimal system characteristics

- The main characteristic of a hexadecimal numbering system is that there are
**16**different counting**digits**ranging from 0 to F. - Each
**digit**of the number has a weight or**value**of 16 starting from the least significant bit. - Since the base of a hexadecimal system is 16, which also represents the number of individual symbols used in the system, the subscript 16 is used to identify a number expressed in hexadecimal.
- Hexadecimal numbers are
**digits**that go from 0 to 9 and then the letters that go from A to F are used. - The
**programmers**use hexadecimal numbers because their values are shorter than they would be if shown in decimal, and much shorter than in binary, which uses only 0 and 1. - The system is also used as an
**HTML color code**to express a specific color. - You can express
**negative numbers**in the same way that you do in the decimal form of a number. - Hexadecimal is a great way to
**compress data**. - It uses the abbreviation ”
**hex**” to be represented.

## History

The choice of the letters A through F to represent the digits greater than nine did not occur universally in the early **history** of **computers** . During the 1950s, some installations favored the use of the digits 0 to 5 with a macron character (“¯”) to denote the values 10-15. However, there were mathematicians who opposed this theory. Bruce A. Martin of Brookhaven National Laboratory considered the choice of AF to be somewhat illogical and in a 1968 letter to the CACM editor proposed a completely new set of symbols based on bit locations, which did not got a lot of acceptance.

## Who Invented the Hexadecimal System

The current hexadecimal system was introduced in the field of **computing** pioneered by **IBM** in 1963. An earlier representation, with 0-9 yu-z, it was used in 1956 by the computer **Bendix G-15** .

## Hexadecimal System Symbols

Because the normal numbering system is in **decimal** or base **ten** , the idea of using the first six letters of the alphabet was adopted to be able to supply the numbers that were needed. In this way, the symbols used in the hexadecimal system are the following:

**S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F ****}**

It should be noted that A = 10, B = 11, C = 12, D = 13, E = 14 and the letter F corresponds to the number 15.

## Examples

For example, the value of the hexadecimal number 1A3F in base 16:

- 1A3F in base 16 = 1 × 16 ^ 3 + Ax16 ^ 2 + 3 × 16 ^ 1 + Fx16 ^ 0
- 1 × 4096 + 10 × 256 + 3 × 16 + 15 × 1 = 6719
- 1A3F in base 16 = 6719 in base 10
- 1735: 16 = 108 Rest: 7
- 108: 16 = 6 Rest: C that is, 12 in base 10
- 6: 16 = 0 Rest: 6