Binary Addition

What you'll learn: How to add binary numbers using simple carry rules—the same logic your computer uses for all arithmetic.

The Core Idea

Binary addition works just like decimal addition you learned in elementary school, but with only two digits (0 and 1). You add column by column from right to left, and when the sum exceeds what one digit can hold, you "carry" to the next column.

The Four Rules

There are only four possible cases when adding two binary digits:

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10  (write 0, carry 1)

The last rule is the important one: when you add 1 + 1, you get 2 in decimal, which is 10 in binary—so you write down 0 and carry 1 to the next column (just like carrying in decimal when 9 + 1 = 10).

Example Walkthrough

Let's add 1011 (11 in decimal) and 0110 (6 in decimal):

    ¹¹    (carries)
   1011
 + 0110
 ------
  10001

• Rightmost column: 1 + 0 = 1
• Second column: 1 + 1 = 0, carry 1
• Third column: 0 + 1 + 1(carry) = 0, carry 1
• Fourth column: 1 + 0 + 1(carry) = 0, carry 1
• New column: carry becomes 1

Result: 10001 (which is 17 in decimal—verify: 11 + 6 = 17 ✓)

Why This Matters

Every calculation your computer performs—whether adding your shopping cart total or rendering graphics—starts with binary addition in the processor's circuits. Understanding this foundation reveals how computers do math at the hardware level.

Key Takeaway: Binary addition follows the same carry principle as decimal addition, but with only 0s and 1s. When 1 + 1 occurs, you get 10 in binary (write 0, carry 1).