Hexadecimal Math Calculator

Calculator

Value A

Value B

Operation

Word size for bitwise view

Input notes

Use 0x, spaces, commas, or underscores if needed.

Signed values

Prefix a value with minus for negative arithmetic.

Formula used

Hexadecimal math uses base sixteen. Each place is a power of sixteen. The value of a hex number is the sum of each digit multiplied by its place value.

Decimal value = d_n × 16ⁿ + d_n-1 × 16^n-1 + ... + d₀ × 16⁰

Arithmetic operations use the same rules as decimal math. Carries and borrows move in groups of sixteen. Bitwise logic works on the binary form of each hex digit.

For a signed word, the highest bit is the sign bit. If it is set, the signed value equals unsigned value minus 2^{word size}.

How to use this calculator

Enter Value A in hexadecimal format. Enter Value B when the selected operation needs two values. Choose an operation from the list. Select a word size for bitwise, signed, and fixed-width output. Press the calculate button. The result appears above the form and below the page header.

Example data table

Value A	Operation	Value B	Hex result	Decimal result
1A	Add	0F	29	41
FF	AND	0F	F	15
20	Subtract	3	1D	29
10	Multiply	A	A0	160
FF	Signed 8 bit view	None	FF	-1

Hexadecimal Math Calculator Guide

Why hexadecimal matters

Hexadecimal notation is common in programming, networking, memory maps, and digital electronics. It uses sixteen symbols, from 0 to 9 and A to F. This compact style makes long binary values easier to read. A byte such as 11111111 becomes FF. That is shorter and clearer.

What this calculator does

This calculator helps you perform hex arithmetic without manual conversion. You can add, subtract, multiply, divide, find remainders, calculate powers, and apply bitwise operations. It also converts results to decimal, binary, and octal. This makes it useful for code checks, register work, color values, data packets, and classroom tasks.

Hex values are treated as whole numbers. The tool first cleans the input. Then it validates each character. For normal arithmetic, it converts valid hex strings to integer values. It then applies the selected operation. The final value is shown again in several number systems. When a word size is selected, the calculator can also show a signed two's complement view.

Bitwise and signed work

Bitwise operations compare binary positions. AND keeps bits that are 1 in both values. OR keeps bits that are 1 in either value. XOR keeps bits that are different. NOT flips bits inside the selected word size. Left shift moves bits toward larger values. Right shift moves bits toward smaller values.

Signed interpretation matters when working with fixed-width registers. For example, FF is 255 as an unsigned byte. The same FF is -1 as a signed 8-bit value. The calculator explains both views when a word size is chosen. This helps reduce errors in embedded code and low-level debugging.

Practical output tips

Use uppercase output when sharing documentation. Use grouped binary output when checking bit fields. Keep values within practical word sizes for dependable bitwise results. Very large numbers may need specialist arbitrary precision libraries. For common 8, 16, 32, and 64 bit work, this page gives quick and clear answers.

The export buttons save the current result. CSV is useful for spreadsheets. PDF is useful for reports, worksheets, and records. The example table below shows typical inputs and results. Compare your own result with these examples before using it in production notes.

Save repeated test cases as durable audit records for careful firmware review. This builds a reliable trail for safer later checks.

FAQs

What is hexadecimal math?

Hexadecimal math is arithmetic in base sixteen. It uses digits 0 to 9 and letters A to F. It is common in programming, memory addresses, digital systems, and bit-level work.

Can I enter lowercase hex digits?

Yes. The calculator accepts lowercase letters and converts them to uppercase internally. It also accepts common separators, such as spaces, underscores, and commas.

Does this calculator support negative values?

Yes. Add a minus sign before a value for signed arithmetic. For fixed-width signed views, choose the correct word size before calculating.

What does word size mean?

Word size is the fixed number of bits used for bitwise output. Common choices are 8, 16, 32, and 64 bits.

Why is FF sometimes 255 and sometimes -1?

FF is 255 as an unsigned 8-bit value. In signed two's complement form, all bits are set, so the same byte represents -1.

Can I calculate bitwise AND, OR, and XOR?

Yes. Select the required bitwise operation. The calculator applies it inside the chosen word size and shows the fixed-width result.

What do the export buttons do?

The CSV button downloads spreadsheet-friendly data. The PDF button creates a simple report with the current operation, result, conversions, and word view.

Can this handle very large hexadecimal numbers?

The arithmetic functions support long values. Very large powers are limited to keep the page responsive. Specialist tools may be better for huge cryptographic numbers.