Binary Addition Rules

Binary addition follows rules similar to decimal addition but only involves two digits: 0 and 1. Here are the basic rules:

1. 0 + 0 = 0
2. 0 + 1 = 1
3. 1 + 0 = 1
4. 1 + 1 = 10 (where 10 is binary for 2, meaning carry over 1)

Steps for Binary Addition

We add binary numbers by adding each bit and handling the carry-over.

Example: Add binary numbers 1011 and 1101.

Steps are as follows:

1. Add each bit from right to left:
   • 1 + 1 = 10 (write down 0, carry over 1)
   • 1 + 0 + 1 = 10 (write down 0, carry over 1)
   • 0 + 1 + 1 = 10 (write down 0, carry over 1)
   • 1 + 1 = 10 (write down 0, carry over 1)
2. Finally, if there is a carry, write it down in front.

The result is:

  1011
+ 1101
------
 11000

Detailed Steps

• Step 1: Add the rightmost bits: 1 + 1 = 10, write down 0, carry over 1.
• Step 2: Add the second bits (including carry): 1 + 0 + 1 = 10, write down 0, carry over 1.
• Step 3: Add the third bits (including carry): 0 + 1 + 1 = 10, write down 0, carry over 1.
• Step 4: Add the leftmost bits (including carry): 1 + 1 = 10, write down 0, carry over 1.