Binary addition works like decimal addition but carries at 2 instead of 10. It is what the adder circuits inside every CPU do billions of times a second.
How to use the Binary Addition Calculator
- Binary number 1
- Binary number 2
- Representation
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Enter two binary numbers. The calculator writes the column addition with the carry row. Choose a bit width to see how the result looks in a fixed-size register and whether it overflows.
Formula
0 + 0 = 0, 0 + 1 = 1, 1 + 1 = 10 (write 0, carry 1), 1 + 1 + 1 = 11
Worked example
Inputs — Binary number 1: 1011; Binary number 2: 111; Representation: Automatic (fit the numbers).
Results — Sum (binary) = 1 0010; Sum (decimal) = 18; Number 1 in decimal = 11; Number 2 in decimal = 7; Long addition = carry 111
01011
+ 00111
─────
10010.
Key terms
- Carry
- A 1 passed to the next column when a column sum is 2 or 3.
Frequently asked questions
What is 1 + 1 in binary?
10.
What is 1011 + 111?
10010 (11 + 7 = 18).
What is overflow?
When the sum needs more bits than the register has.
How do I check a binary sum?
Convert both numbers and the result to decimal.