Hexadecimal Calculator & Converter

How to Calculate with Hexadecimal Numbers

Hexadecimal (base-16) calculations involve numbers and letters A-F. Here's a guide on performing hexadecimal calculations:

Conversion Formula

To convert between hexadecimal and decimal:

• Hex to Decimal: \( \sum_{i=0}^{n-1} d_i \times 16^i \)
• Decimal to Hex: Repeatedly divide by 16 and track remainders

Where \(d_i\) is the decimal value of each hex digit, and \(i\) is its position from right to left.

Calculation Steps

1. Convert hex numbers to decimal
2. Perform the arithmetic operation in decimal
3. Convert the result back to hexadecimal

Example: Adding 1A and 2B in Hexadecimal

Step 1: Convert to Decimal

1A = 1×16¹ + 10×16⁰ = 16 + 10 = 26

2B = 2×16¹ + 11×16⁰ = 32 + 11 = 43

Step 2: Add in Decimal

26 + 43 = 69

Step 3: Convert Result to Hexadecimal

69 ÷ 16 = 4 remainder 5

4 ÷ 16 = 0 remainder 4

Reading remainders bottom-up: 45

Final Result

1A + 2B = 45 (in hexadecimal)

Visual Representation

This diagram illustrates the process of adding hexadecimal numbers 1A and 2B to get the result 45.