Convert Hexadecimal to Decimal

Hexadecimal (base 16) uses digits 0-9 and letters A-F, where A=10, B=11, C=12, D=13, E=14, and F=15. Converting hex to decimal follows the same positional notation principle as binary, but using powers of 16 instead of 2.

Step-by-step example — converting 1A3F to decimal:

1. Write each digit with its position (right to left): 1(3) A(2) 3(1) F(0)
2. Replace letters with values: 1(3) 10(2) 3(1) 15(0)
3. Multiply by powers of 16: 1×16³ + 10×16² + 3×16¹ + 15×16⁰
4. Calculate: 4096 + 2560 + 48 + 15 = 6719

So 0x1A3F = 6719₁₀.

Why hexadecimal is important:

Hex is widely used in computing because it provides a compact representation of binary data. Each hex digit maps to exactly 4 binary bits, making conversion between hex and binary trivial. A single byte (8 bits) is always exactly 2 hex digits, which is far easier to read than 8 binary digits.

Common hex values you should recognize:

• 0xFF = 255 — maximum value of a single byte
• 0x100 = 256 — one more than a byte can hold
• 0xFFFF = 65535 — maximum 16-bit unsigned value
• 0x7FFFFFFF = 2147483647 — maximum 32-bit signed integer
• 0xDEADBEEF = 3735928559 — classic magic number used in debugging

Programming shortcuts:

Most languages accept hex literals directly. In JavaScript, 0x1A3F evaluates to 6719. In Python, int("1A3F", 16) returns the same result. The 0x prefix is a universal convention indicating a hexadecimal number. Understanding hex-to-decimal conversion is essential for reading memory dumps, debugging binary protocols, and working with color codes.