Number SystemFree Interactive Tool

Decimal to Hexadecimal

Convert base-10 decimal numbers into hexadecimal notation (0-9, A-F) with repeated 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)

Decimal Number (Base 10)

Enter any non-negative base 10 integer.

Calculated Output

Primary Representation

Calculating...

Step-by-Step Mathematical Proof

Active Derivation

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Concept

What Is Decimal to Hexadecimal?

Decimal to hexadecimal conversion transforms base-10 numbers into base-16 notation. Hexadecimal uses sixteen symbols: 0 to 9 followed by A (10), B (11), C (12), D (13), E (14), and F (15).

Methodology

How Does It Work?

Repeatedly divide the decimal number by 16. Record the remainders (0-15), converting any remainder >= 10 into its corresponding letter (A-F). Continue until quotient is 0 and read remainders from bottom to top.

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 254 to hexadecimal: 254 / 16 = 15 remainder 14 (E) 15 / 16 = 0 remainder 15 (F) Reading bottom to top gives: FE_{16}.

Important Rules & Edge Cases

Remainders 10, 11, 12, 13, 14, 15 map to A, B, C, D, E, F.
Hex values are often prefixed with 0x in programming languages.

Practical Applications in Engineering

Defining HTML and CSS color codes (e.g. RGB 255, 0, 128 -> #FF0080).
Representing computer memory addresses and pointer values.
Specifying machine codes in disassemblers and debugging tools.

Common Mistakes to Avoid

Caution: Leaving remainders greater than 9 as numbers instead of converting to letters (e.g., writing 1514 instead of FE).
Caution: Dividing by 10 instead of 16.

FAQ