Hexadecimal ToolsFree Interactive Tool

Hexadecimal Multiplication

Multiply hexadecimal numbers with base-16 partial products 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 values (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 Multiplication?

Hexadecimal multiplication calculates the product of two base-16 numbers using partial products computed in radix 16.

Methodology

How Does It Work?

Multiply each digit of the multiplier by each digit of the multiplicand. Convert products >= 16 into a base-16 quotient (carry) and remainder. Sum partial products using hex addition.

Formula & Rules

Mathematical Algorithm

A_{16} \times B_{16} = \text{Product}_{16}

Worked Problem

Step-by-Step Example

Multiply 1A_{16} (26) × 0B_{16} (11): B (11) × A (10) = 110 -> 110/16 = 6 remainder 14 (E) -> write E, carry 6 B (11) × 1 + 6 (carry) = 17 -> 17/16 = 1 remainder 1 -> write 1, carry 1 -> 11E_{16} Result: 11E_{16} (decimal 286).

Important Rules & Edge Cases

Column products wrap at 16.
Partial products shift left by one hex position (multiplication by 16) for each row.

Practical Applications in Engineering

Multi-precision arithmetic in cryptographic key generators (ECC, RSA).
Memory stride calculations in computer graphics rasterizers.
Compiler loop unrolling and address indexing optimization.

Common Mistakes to Avoid

Caution: Multiplying digits in decimal without converting the intermediate product back to base 16.
Caution: Forgetting carries from previous digit multiplications.

FAQ