# Use of Hexadecimal Numbers in Computer Science

## How do we define a hexadecimal number system?

The hexadecimal numeral system is a method of representing numbers using a base of sixteen. Unlike the decimal system, which uses ten symbols to represent values from zero to nine, hexadecimal uses sixteen symbols, including "0" to "9" for values zero to nine, and "A" to "F" (or "a" to "f") for values ten to fifteen.

### Example

In the hexadecimal system the number 1234 is represented as:

4 D 2

(4x16²) + (13x16¹) + (2x16⁰)

1024 + 208 + 2 = 1234

Where 16⁰ = 1.

## Why do we use hexadecimal number systems?

To answer this question we need to look at how data is stored in a computers memory.

## How is data stored in a computers memory?

Binary numbers (base-2), which computers fundamentally use, tend to be long and cumbersome. Hexadecimal (base-16) numbers are much shorter, making them easier to read and write. Each hex digit represents four binary digits (bits), so a single byte (8 bits) can be represented by just two hex digits.

## Ok, so we can use hexadecimal numbers to simplify working with memory.

## What else can we do with them?

### Human Readability

Hexadecimal numbers are easier for humans to read and interpret than binary numbers. Many computer scientists and engineers find it simpler to work with smaller hex numbers compared to lengthy binary strings.

### Eliminating Redundancy

Hexadecimal offers a high-density representation of data. For example, while a 32-bit binary number requires 32 digits to write out, the same number can be represented by just 8 hex digits, thus saving space and reducing the potential for errors when reading or transcribing.

### Memory Address

Memory addresses in computing are typically long binary numbers, but representing these in hex simplifies their notation. This is particularly useful in debugging, where memory locations and contents are commonly displayed.

### Easy Conversion to Binary

Converting between binary and hexadecimal is straightforward. Each hex digit corresponds directly to a four-bit binary sequence, making the conversion process simple and fast. For example, the binary sequence 1010 1100 can be quickly converted to the hex value AC.

### Intuitive Mapping to a Byte in Memory

Given that hexadecimal digits map neatly to four-bit nibbles (a half-byte), hexadecimals align perfectly with the byte-oriented architecture of modern computers. This alignment facilitates various low-level programming tasks, such as setting flags and manipulating memory.

### Standardization

Hexadecimal numbers have become a standard way to denote binary data in documentation, programming, and networking. For instance, color codes in web design, machine code for microprocessors, and IP addresses in certain contexts use hex notation, making it a universally understood format among professionals.

#### RGB Color Codes Example

#### Machine Code Example

#### IP Address

### Debugging and Diagnostics

Tools like debuggers and hex editors display data in hexadecimal format because it allows developers to quickly recognize patterns, offsets, and memory addresses. This is particularly useful when dealing with low-level system data or interfacing directly with hardware.

### Checksum and Hash Functions

Algorithms that produce checksums, hashes, and cryptographic keys often output results in hexadecimal format for more compact and readable representations. This is practical for ensuring data integrity and security.

### Historical contexts

Historically, hexadecimal has been used in various programming languages and platforms (such as assembly languages and older mainframe systems) due to its efficiency and effectiveness. This legacy continues to influence its ongoing usage in modern computing.

## Summary

In summary, the hexadecimal number system strikes a balance between the binary system used internally by computers and the need for a more compact, readable, and manipulable format for humans. Its ease of conversion, alignment with the binary system, and widespread adoption make it indispensable in computer science.

Thanks for reading!