Method: Adding 8-Bit Binary Numbers

Adding Binary Numbers

Here's how to add two 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 (0 + 0, 0 + 1, 1 + 0, 1 + 1) following these rules:
   • 0 + 0 = 0
   • 0 + 1 = 1
   • 1 + 0 = 1
   • 1 + 1 = 0, carry 1
   • 1 + 1 + 1(carry) = 1, carry 1
3. Check for carry:
   • If the sum of two digits is 1, write down 1 as the result digit.
   • If the sum is 2 (1 + 1), write down 0 as the result digit and carry 1 to the next column.
4. Add the carry: If there's a carry from the previous column, add it to the sum of the next digit pair 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 two 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.

Examples

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

	carry:  111
            0011 0101 
	+       0101 1010
	-----------------
	answer: 1000 1111 
    -----------------