Hex Calculator

Hex Calculator

Hex Calculator

Hex Converter

First Number:

Second Number:

Hex Calculator

Use this Hex Calculator to perform arithmetic operations on hexadecimal numbers. It also allows you to convert base-16 numbers into decimal, octal, and binary formats. Before we dive into operations, let’s understand the hexadecimal system.

What is the Hexadecimal System?

The hexadecimal system is a base-16 number system commonly used in computing. It uses digits 0–9 and letters A–F to represent values from 0 to 15. Like binary (base 2), octal (base 8), and decimal (base 10), hexadecimal simplifies large binary numbers into a human-readable format.

Operations on Hexadecimal Numbers

Hexadecimal Addition

Adding hexadecimal numbers works like decimal addition but with base 16. You can also use a Hex Addition Calculator for quick results.

Example:

Add (2BC)₁₆ + (A56)₁₆

Step-by-Step:

C + 6 = 12 + 6 = 18 → divide by 16 → Remainder = 2, Carry = 1
Carry + B + 5 = 1 + 11 + 5 = 17 → divide by 16 → Remainder = 1, Carry = 1
Carry + 2 + A = 1 + 2 + 10 = 13 → D in hex

Answer: D12₁₆

Hexadecimal Subtraction

Hex subtraction works like decimal subtraction, considering base 16.

Example:

Subtract (BA)₁₆ - (A3)₁₆

Step-by-Step:

A - 3 = 7
B - A = 1

Answer: 17₁₆

Hexadecimal Multiplication

Hex multiplication uses base 16. A calculator is recommended for speed, but manual steps help understanding.

Example:

Multiply (BA)₁₆ × (A3)₁₆

Step-by-Step:

3 × C = 39 → divide by 16 → Remainder = 7, Carry = 2
2 × D + carry = 26 + 1 = 27 → divide by 16 → Remainder = 11 = B, Carry = 1
Add remaining values → Result = 4F7₁₆

Hexadecimal Division

Hex division can be done in three ways:

Directly divide hexadecimal numbers.
Convert to decimal, divide, and convert back.
Use an online Hex Calculator for instant results.

Hexadecimal Conversions

Hexadecimal to Decimal

Multiply each digit by 16 raised to its positional power and sum the results.

Example:

Convert (A69)₁₆ to decimal:

\[ (A69)_{16} = 10*16^2 + 6*16^1 + 9*16^0 = 2560 + 96 + 9 = 2665_{10} \]

Decimal to Hexadecimal

Divide the decimal number by 16 repeatedly and write the remainders in reverse order.

Example:

Convert (266)₁₀ to hexadecimal:

\(266 ÷ 16 = 16\) remainder 10 → 10 = A → Result: 10A₁₆

Hexadecimal to Binary

Each hex digit corresponds to 4 binary digits. Use the table below:

Hex	Binary
0	0000
1	0001
2	0010
3	0011
4	0100
5	0101
6	0110
7	0111
8	1000
9	1001
A	1010
B	1011
C	1100
D	1101
E	1110
F	1111

Binary to Hexadecimal

Group binary digits into sets of 4 starting from the right, then convert each group to its hex equivalent using the table above.

How Hex Calculator Works

Input:

Select an operation or conversion type from the dropdown.
Enter hexadecimal numbers in the provided fields.
Click “Calculate” to get results.

Output:

Result of operations (Addition, Subtraction, Multiplication, Division)
Conversion of hex numbers to Binary, Decimal, and Octal

FAQs

Why is the hexadecimal system used?

It provides a human-friendly representation of binary data, making it easier for programmers and system designers to read and process large numbers efficiently.

What is a 64-digit hexadecimal number?

The maximum value of a 64-bit hex number is 18,446,744,073,709,551,615. You can verify this using our Hex Calculator.

Difference between ASCII and hexadecimal?

ASCII is a code representing characters (0–255 decimal / 00–FF hex). Hexadecimal is a base-16 number system used for numerical representation.

What is FFFF in decimal?

FFFF₁₆ = 65535₁₀.

Conclusion

Hexadecimal simplifies the representation of large numbers, reduces digits required compared to binary or decimal, and is essential in computing. Our free Hex Calculator lets you perform operations and conversions quickly and accurately.

Hex Calculator

Hex Calculator

What is the Hexadecimal System?

Operations on Hexadecimal Numbers

Hexadecimal Addition

Example:

Hexadecimal Subtraction

Example:

Hexadecimal Multiplication

Example:

Hexadecimal Division

Hexadecimal Conversions

Hexadecimal to Decimal

Example:

Decimal to Hexadecimal

Example:

Hexadecimal to Binary

Binary to Hexadecimal

How Hex Calculator Works

FAQs

Why is the hexadecimal system used?

What is a 64-digit hexadecimal number?

Difference between ASCII and hexadecimal?

What is FFFF in decimal?

Conclusion

References