HEX to Decimal Converter

Decimal (Denary) System

The decimal system is the most commonly used number system in everyday life, based on the number 10. It includes digits from 0 to 9. Each position in a decimal number represents a power of 10.

Example

For the number 347, the place values are:
3 × 10² = 3004 × 10¹ = 407 × 10⁰ = 7So, 347 in decimal is simply the sum of these: 300 + 40 + 7 = 347.

Hexadecimal (Base-16) System

The hexadecimal system is a base-16 system. It uses the digits 0-9 and the letters A-F to represent values 10 through 15. This system is widely used in computing and digital electronics because its a compact way to express binary data.

Example

In the hexadecimal number A2B:
A represents 10, 2 represents 2, and B represents 11.

Converting Hexadecimal to Decimal

To convert a hexadecimal number to decimal, each hex digit is multiplied by 16 raised to the power of its position (starting from 0 on the right).

Example

Convert A2B₁₆ to decimal:
A × 16² = 10 × 256 = 25602 × 16¹ = 2 × 16 = 32B × 16⁰ = 11 × 1 = 11So, A2B₁₆ equals 2603₁₀.

Decimal to Binary Conversion

Converting decimal numbers to binary involves repeatedly dividing the number by 2 and noting the remainders.

Example

Convert 2603₁₀ to binary:
2603 ÷ 2 = 1301 (remainder: 1)1301 ÷ 2 = 650 (remainder: 1)650 ÷ 2 = 325 (remainder: 0)325 ÷ 2 = 162 (remainder: 1)... (continue dividing)Reading the remainders from bottom to top gives the binary equivalent: 101000101011₂.

Hexadecimal to Binary Conversion

Hexadecimal numbers can be directly converted to binary by substituting each hex digit with its corresponding 4-bit binary value.

Example

Convert A2B₁₆ to binary:
A = 1010₂2 = 0010₂B = 1011₂So, A2B₁₆ = 101000101011₂.

Using an Online Hexadecimal Converter

Using an online hex converter simplifies these processes, especially for beginners. By inputting a hexadecimal number, the converter provides instant results for both decimal and binary conversions, saving time and minimizing errors.

Try it now: Use our hexadecimal converter tool to perform quick conversions online.

Why Understanding These Systems Matters

Mastering the hexadecimal, decimal, and binary systems is critical for fields like programming, digital electronics, and data science. These systems form the backbone of data representation in computers, making them an essential part of any technical skill set.

Related Topics for Further Learning

• Hexadecimal Numbers: Understanding their role in memory addressing and color codes.
• Binary Systems: Learn how binary represents data in computer architecture.
• Denary Numbers: A deeper look into the decimal system and its applications in real-world scenarios.