The base-16 system.
Hex uses 16 symbols: digits 0–9 plus letters A–F representing 10–15. Each position is a power of 16 — making hex 4× more compact than binary for the same value.
The Math
How hex to decimal conversion works.
Hexadecimal is base-16. Each digit position represents a power of 16. Converting to decimal means multiplying each digit by its positional power of 16 and summing the results.
← Try the live converterPositional multiplication.
For 1A3F: compute 1×16³ + A×16² + 3×16¹ + F×16⁰ = 4096 + 2560 + 48 + 15 = 6719. Each digit's value multiplied by its place value.
Sum the products.
Add every term together. The result is the exact decimal integer that represents the same quantity as the original hex string. Use the calculation steps toggle in the converter to trace any conversion.
Worked examples.
FF→255
F (position 1)15 × 16¹ = 240
F (position 0)15 × 16⁰ = 15
Sum240 + 15 = 255
1A3F→6,719
1 (position 3)1 × 16³ = 4,096
A (position 2)10 × 16² = 2,560
3 (position 1)3 × 16¹ = 48
F (position 0)15 × 16⁰ = 15
Sum4,096 + 2,560 + 48 + 15 = 6,719
DEADBEEF→3,735,928,559
Famous debug placeholder used in Microsoft tools. Each nibble maps to a letter or digit: D=13, E=14, A=10, D=13, B=11, E=14, E=14, F=15. The 8-digit hex value sums to exactly 3,735,928,559 decimal.
Powers of 16 reference.
These are the positional weights you multiply each hex digit by:
| Position | Power of 16 | Decimal Value | Binary Bits |
|---|---|---|---|
| 0 | 16⁰ | 1 | 4 bits |
| 1 | 16¹ | 16 | 8 bits |
| 2 | 16² | 256 | 12 bits |
| 3 | 16³ | 4,096 | 16 bits |
| 4 | 16⁴ | 65,536 | 20 bits |
| 5 | 16⁵ | 1,048,576 | 24 bits |
| 6 | 16⁶ | 16,777,216 | 28 bits |
| 7 | 16⁷ | 268,435,456 | 32 bits |