Hexadecimal Number System

Hexadecimal Number System

The hexadecimal number system (or hex) is a base-16 number system that uses 16 symbols to represent values. It’s commonly used in computing and digital electronics because it provides a more human-friendly representation of binary-coded values. Hexadecimal is particularly useful in representing memory addresses, colors in web development, and various low-level programming tasks.

Symbols in Hexadecimal

In the hexadecimal system:

• The digits 0-9 represent values 0-9.
• The letters A-F represent values 10-15.

For example:

• A in hex represents 10 in decimal.
• F in hex represents 15 in decimal.

Hexadecimal Number Representation

Hexadecimal numbers can include both digits and letters. Some examples include:

• 1A3 in hex is equal to 1 * 16^2 + 10 * 16^1 + 3 * 16^0 = 419 in decimal.
• FF in hex is equal to 15 * 16^1 + 15 * 16^0 = 255 in decimal.

Conversion Between Hexadecimal and Other Number Systems

Hexadecimal to Decimal:

• To convert a hexadecimal number to decimal, multiply each digit by the corresponding power of 16 based on its position and sum the results.

Decimal to Hexadecimal:

• To convert a decimal number to hexadecimal, repeatedly divide the decimal number by 16, recording the remainder at each step. The hex number is formed by combining the remainders.

Hexadecimal to Binary:

• Each hex digit can be directly converted into a 4-bit binary number. For instance:
  • A (10 in decimal) is 1010 in binary.
  • F (15 in decimal) is 1111 in binary.

Binary to Hexadecimal:

• Group the binary digits in sets of four (starting from the right). Convert each 4-bit group to its corresponding hexadecimal digit.

Applications of Hexadecimal

• Memory Addressing: Hexadecimal is often used in computing for memory addresses since it’s more compact than binary and easier to read.
• Color Representation: In web development, colors are commonly represented using hex codes. For example, #FF5733 is a shade of orange.
• Assembly Language Programming: Hexadecimal is frequently used in assembly languages and low-level programming because it aligns well with the binary system used by computers.

Example Conversions

• Hexadecimal 2F to decimal:
  • 2 * 16^1 + 15 * 16^0 = 32 + 15 = 47 in decimal.
• Decimal 255 to hexadecimal:
  • 255 / 16 = 15 remainder 15 → FF in hex.

Conclusion

The hexadecimal number system is an essential part of computing and electronics, offering a concise way to represent large binary numbers. Understanding hex is crucial for tasks ranging from debugging low-level code to working with web colors.

For a detailed step-by-step explanation, check out the full article: https://www.geeksforgeeks.org/hexadecimal-number-system/.