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Decimal to Hex

Convert decimal integers into hexadecimal strings with successive division by 16. Designed for software developers, electrical engineers, students, and computer architecture researchers requiring deterministic client-side accuracy.

Engine: Client-Side Verified (0ms Latency)

Enter any non-negative base 10 integer.

Calculated Output

Primary Representation
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Step-by-Step Mathematical Proof

Active Derivation
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Concept

What Is Decimal to Hex?

Decimal to hex conversion transforms standard base-10 numbers into base-16 hexadecimal strings.

Methodology

How Does It Work?

Divide the decimal number repeatedly by 16. Record remainders, mapping 10-15 to A-F. Read remainders bottom to top to assemble the hex string.

Formula & Rules

Mathematical Algorithm

Q_k = \lfloor Q_{k-1} / 16 \rfloor, \quad r_k = Q_{k-1} \pmod{16}
Worked Problem

Step-by-Step Example

Convert 175 to hex: 175 / 16 = 10 remainder 15 (F) 10 / 16 = 0 remainder 10 (A) Reading bottom to top gives: AF_{16}.

Important Rules & Edge Cases

  • Remainders from 10 to 15 map to A through F.
  • Only valid base-10 digits 0-9 are accepted in input.

Practical Applications in Engineering

  • Generating hex color codes from RGB decimal channels (0-255).
  • Formatting pointer addresses in debugging logs.
  • Writing binary firmware patch files.

Common Mistakes to Avoid

  • Caution: Writing remainders greater than 9 as numbers instead of letters (e.g. writing 1015 instead of AF).
  • Caution: Dividing by 10 instead of 16.
FAQ

Frequently Asked Questions

What is 100 in hex?

100 in decimal equals 64 in hexadecimal (6×16 + 4 = 100).