NumForge LogoNumForge
Explore
Base Conversion ToolsFree Interactive Tool

Base-16 Converter

Convert numbers into and out of hexadecimal (base 16) across any custom radix. Designed for software developers, electrical engineers, students, and computer architecture researchers requiring deterministic client-side accuracy.

Engine: Client-Side Verified (0ms Latency)

Enter hex characters (0-9, A-F).

Calculated Output

Primary Representation
Calculating...

Step-by-Step Mathematical Proof

Active Derivation
Ready. Enter input above to generate derivation.
Concept

What Is Base-16 Converter?

Base 16 (hexadecimal) uses sixteen characters: 0 through 9 and A through F. Each hex character aligns directly with a 4-bit binary nibble.

Methodology

How Does It Work?

Expands digits using powers of 16 or maps directly to 4-bit binary nibbles.

Formula & Rules

Mathematical Algorithm

N_{10} = \sum d_i 16^i
Worked Problem

Step-by-Step Example

Convert 1F4_{16} to decimal: (1 × 256) + (15 × 16) + (4 × 1) = 256 + 240 + 4 = 500_{10}.

Important Rules & Edge Cases

  • A through F represent 10 through 15.

Practical Applications in Engineering

  • Memory pointers, web colors, byte manipulation.

Common Mistakes to Avoid

  • Caution: Treating F as 16 instead of 15.
FAQ

Frequently Asked Questions

What is 16 in base 16?

16 in decimal is written as 10 in base 16.