What is Hexadecimal?

Table of Contents

Introduction

Hexadecimal, often abbreviated as hex, is a base-16 numeral system. Unlike the decimal system, which uses ten digits (0–9), hexadecimal uses sixteen symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. It’s widely used in computing as a more human-readable representation of binary numbers, simplifying the way large binary values are expressed.

How Hexadecimal Works

Each position in a hexadecimal number corresponds to a power of 16, starting from ( 16^0 ) at the rightmost position.

Example:
Hexadecimal: 2A3
Calculation:
(2 × 162) + (10 × 161) + (3 × 160)
= 512 + 160 + 3
= 675 (decimal)

In computing, hexadecimal is often used to represent binary values more compactly since one hexadecimal digit corresponds to exactly four binary bits.

Hexadecimal vs. Decimal and Binary

Feature Hexadecimal (Base-16) Decimal (Base-10) Binary (Base-2)
Symbols Used 0–9, A–F 0–9 0, 1
Representation Powers of 16 Powers of 10 Powers of 2
Example Value 2A = 42 42 101010

Applications of Hexadecimal in Computing

Memory Addressing
Hexadecimal is commonly used to represent memory addresses in programming because it’s more compact and easier to read than binary.

Color Codes
In web design, colors are often defined using hexadecimal codes. For instance:

  • #FFFFFF represents white (Red: 255, Green: 255, Blue: 255).
  • #000000 represents black (Red: 0, Green: 0, Blue: 0).

Error Codes
System and application errors often use hexadecimal codes for debugging.

Machine Language
Hexadecimal simplifies representing large binary sequences used in assembly and machine language.

Converting Between Hexadecimal, Decimal, and Binary

Hexadecimal to Decimal
(3 × 161) + (14 × 160)
= 48 + 14
= 62 (decimal)

Hexadecimal to Binary
Replace each hex digit with its 4-bit binary equivalent.
Example: Convert 2F to binary.
2 = 0010
F = 1111
Result: 2F in binary is 00101111

Binary to Hexadecimal
Group binary digits in sets of four (from right to left) and convert each group to a hex digit.
Example: Convert 11011011 to hexadecimal.
Group: 1101 1011
Convert: 1101 = D, 1011 = B
Result: 11011011 in hex is DB

Conclusion

Hexadecimal is an essential numeral system in computing, offering a compact and readable way to represent binary data. Its applications, from memory addressing to color representation, highlight its importance in technology. By understanding hexadecimal, you gain a deeper insight into how computers operate at a fundamental level.