Method: Adding 3, 8-Bit Binary Numbers

Adding Binary Numbers

Here's one method for adding 3, 8-bit binary numbers:

1. Line up the numbers: Write the binary numbers vertically, aligning the rightmost digits (least significant bits). Use zeros to pad shorter numbers.
2. Add each digit pair: Add the corresponding digits following these rules:
   • 0 + 0 + 0 = 0
   • 0 + 0 + 1 = 1
   • 0 + 1 + 0 = 1
   • 1 + 0 + 0 = 1
   • 0 + 1 + 1 = 0, carry 1 (decimal equiv = 2)
   • 1 + 1 + 0 = 0, carry 1 (decimal equiv = 2)
   • 1 + 1 + 1 = 1, carry 1 (decimal equiv = 3)

   we need to also bring in the carry values

• 1 + 1 + 1 + 1 = 0, double carry 1 (decimal equiv = 4)
• 1 + 1 + 1 + 1 + 1 = 1, double carry 1 (decimal equiv = 5)
3. Check for carry:
   • If the sum of three digits is 1, write down 1 as the result digit.
   • If the sum is 2 (1 + 1 + 0), write down 0 as the result digit and carry 1 to the next column.
   • If the sum is 3 (1 + 1 + 1), write down 1 as the result digit and carry 1 to the next column.
   • If the sum is 4 (1 + 1 + 1 + 1 in the carry row), write down 0 as the result digit and carry 10 to the next two columns. This is like carrying the 1 twice. in reaslity it is carrying 10 where the 0 goes into the next column and the 1 goes in the column after that (a double carry for the 1).
4. Add the carry: If there's a carry from the previous column, add it to the sum of the next digits before checking for carry again.
5. Repeat steps 2-4: Continue adding digits and checking for carry until you reach the leftmost digits.

Carry Forward

Carry forward happens when adding binary digits results in a sum greater than 1. In such cases:

• You write down 0 as the result digit for the current column.
• You carry 1 to the next column on the left.
• This "carried 1" is essentially added to the next digit pair in the next column.
• If the primary carry is full as a result of a previous double carry, put the next carry into the secondary carry slot

Examples

Here are some examples of adding 8-bit binary numbers: