Base-N Addition Calculator

How to Use This Calculator

To add numbers in any base (n), follow these steps:

1. Enter the first number in the "First Number" field.
2. Enter the second number in the "Second Number" field.
3. Select the base (n) from the dropdown menu (2-36).
4. Click "Calculate" to see the result.
5. Use the "Reset" button to clear all fields.

The calculator will display the sum in the selected base and show the calculation steps.

How Base-N Addition Works

Base-n addition follows the same principles as decimal addition but uses a different digit set. Here's how it works:

1. Align the numbers by their least significant digit (rightmost digit).
2. Add the digits from right to left, carrying over when the sum reaches or exceeds the base.
3. Continue until all digits are processed.
4. The result is the sum in the selected base.

For example, adding 1A (hexadecimal) and 2B (hexadecimal) in base-16:

• 1A in decimal is 26
• 2B in decimal is 43
• Sum in decimal is 69
• 69 in hexadecimal is 45

Worked Examples

Example 1: Binary Addition

Add 1011 (binary) and 1101 (binary) in base-2:

1. Align the numbers: 1011 and 1101
2. Add from right to left:
   • 1 + 1 = 10 (write 0, carry 1)
   • 1 (carry) + 1 + 0 = 10 (write 0, carry 1)
   • 1 (carry) + 0 + 1 = 10 (write 0, carry 1)
   • 1 (carry) + 1 + 1 = 11 (write 1, carry 1)
3. Final result: 11000 (binary)

Example 2: Hexadecimal Addition

Add 1A (hexadecimal) and 2B (hexadecimal) in base-16:

1. Convert to decimal:
   • 1A = 1×16 + 10 = 26
   • 2B = 2×16 + 11 = 43
2. Sum in decimal: 26 + 43 = 69
3. Convert 69 to hexadecimal:
   • 69 ÷ 16 = 4 with remainder 5
   • So, 69 = 45 in hexadecimal