Hexadecimal to Decimal Converter

What is Hexadecimal?

The hexadecimal (or base-16) number system uses sixteen distinct symbols to represent values. It employs the digits 0-9 to represent values zero to nine, and the letters A-F to represent values ten to fifteen. Hexadecimal is widely used in computing because it provides a more compact and human-readable representation of binary data.

History of Hexadecimal

The earliest known use of base-16 was by the mathematician Gottfried Wilhelm Leibniz in the late 17th century. Leibniz, who is also known for developing calculus and the binary system, initially called it "sedecimal." Throughout the centuries, it has been referred to by various names, including sedecimal, sexdecimal, and sedenary.

Hexadecimal as we know it today became widely used in the computing era. The term "hexadecimal" first appeared in technical documentation in 1950 when it was used for inputting numbers and instructions into the Standards Eastern Automatic Computer (SEAC), designed by the National Bureau of Standards in the United States.

Why Use Hexadecimal?

There are several compelling reasons why hexadecimal is extensively used in computing:

• Efficient Binary Representation: Each hexadecimal digit represents exactly four binary bits, making conversion between hexadecimal and binary straightforward. This makes it an ideal shorthand for representing binary data.
• Compact Notation: Hexadecimal requires fewer digits than binary for representing the same value. For example, the binary number 11010110 can be expressed as D6 in hexadecimal.
• Memory Addressing: In computing, memory addresses are often expressed in hexadecimal because they efficiently represent byte values and memory locations.
• Color Representation: In web design and digital graphics, colors are typically defined using hexadecimal notation (e.g., #FF0000 for red), where each pair of digits represents the intensity of red, green, and blue components.
• Error Identification: Hexadecimal is used to define memory locations of errors, which helps programmers find and fix issues more efficiently.

Hexadecimal Notation

To distinguish hexadecimal numbers from other number systems, various prefixes or suffixes are commonly used:

Understanding the structure and purpose of hexadecimal numbers is the first step in mastering conversion techniques. The following sections will explain the detailed process of converting hexadecimal to decimal values.