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Hex Calculator

Hex Converter

Hex Calculator

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Hex Calculator

Use this Hex Calculator to perform arithmetic operations on hexadecimal numbers. You can also convert hexadecimal numbers into decimal, octal, and binary formats. Before performing 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 0–15. 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

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

Example:

Add (2BC)₁₆ + (A56)₁₆

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

Example:

Subtract (BA)₁₆ - (A3)₁₆

A - 3 = 7
B - A = 1

Answer: 17₁₆

Hexadecimal Multiplication

Example:

Multiply (BA)₁₆ × (A3)₁₆

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

Hexadecimal Division

Hex division can be performed by:

Directly dividing hexadecimal numbers.
Converting to decimal, dividing, then converting back.
Using 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:

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

Decimal to Hexadecimal

Divide the decimal number repeatedly by 16 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:

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 (from right to left) and convert each group to hex using the table above.

How Hex Calculator Works

Input:

Select an operation or conversion type.
Enter hexadecimal numbers in the fields.
Click "Calculate" for results.

Output:

Results of operations (Addition, Subtraction, Multiplication, Division)
Hex conversions to Binary, Decimal, and Octal

FAQs

Why is the hexadecimal system used?

Hexadecimal provides a human-friendly way to represent binary data, making it easier to read and process large numbers efficiently.

What is a 64-digit hexadecimal number?

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

Difference between ASCII and hexadecimal?

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

What is FFFF in decimal?

FFFF₁₆ = 65535₁₀

Conclusion

Hexadecimal simplifies large numbers, reduces digit count compared to binary/decimal, and is essential in computing. Our free Hex Calculator provides fast, accurate operations and conversions.

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