Hexadecimal ToolsFree Interactive Tool

Hexadecimal Subtraction

Subtract hexadecimal numbers with column borrows of 16 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)

Minuend Hex (A)

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

Subtrahend Hex (B)

Calculated Output

Primary Representation

Calculating...

Step-by-Step Mathematical Proof

Active Derivation

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Concept

What Is Hexadecimal Subtraction?

Hexadecimal subtraction finds the difference between two base-16 numbers. When subtracting a larger digit from a smaller one, a borrow from the next higher column provides 16.

Methodology

How Does It Work?

Subtract digits column by column from right to left. If top digit < bottom digit, borrow 1 from the next non-zero column to the left (worth 16), add 16 to the top digit, then subtract.

Formula & Rules

Mathematical Algorithm

A_{16} - B_{16} = \text{Diff}_{16} \quad \text{with borrow of 16}

Worked Problem

Step-by-Step Example

Subtract 3B2_{16} - 1F4_{16}: Column 0: 2 - 4 (borrow 1 from B -> B becomes A, 2 becomes 2+16=18) -> 18 - 4 = 14 (E) Column 1: A (10) - F (15) (borrow 1 from 3 -> 3 becomes 2, A becomes 10+16=26) -> 26 - 15 = 11 (B) Column 2: 2 - 1 = 1 Result: 1BE_{16}.

Important Rules & Edge Cases

A borrow from the adjacent higher column adds 16 to the borrowing column.
Only valid hex characters 0-9 and A-F are allowed.

Practical Applications in Engineering

Determining memory buffer sizes and address spans (end_address - start_address).
Calculating relative offsets in assembly code jump instructions.
Low-level kernel memory management.