Hexadecimal ToolsFree Interactive Tool

Hexadecimal Addition

Add hexadecimal numbers with column carries, base-16 wrapping, and step-by-step proofs. Designed for software developers, electrical engineers, students, and computer architecture researchers requiring deterministic client-side accuracy.

Engine: Client-Side Verified (0ms Latency)

First Hex Number (A)

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

Second Hex Number (B)

Calculated Output

Primary Representation

Calculating...

Step-by-Step Mathematical Proof

Active Derivation

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Concept

What Is Hexadecimal Addition?

Hexadecimal addition computes the sum of two base-16 numbers. A column sum of 16 or greater produces a carry of 1 to the next column, leaving sum - 16 in the current column.

Methodology

How Does It Work?

Add digits column by column from right to left in base 16. If column sum >= 16, subtract 16 and carry 1 to the next column. Map results >= 10 to A through F.

Formula & Rules

Mathematical Algorithm

A_{16} + B_{16} = \text{Sum}_{16} \quad \text{with carry when } \text{sum}_i \ge 16

Worked Problem

Step-by-Step Example

Add 1A4_{16} + 2F_{16}: Column 0: 4 + F (15) = 19 -> 19 - 16 = 3, carry 1 Column 1: A (10) + 2 + 1 (carry) = 13 -> D Column 2: 1 Result: 1D3_{16} (decimal 467).