Calculate The 8-Bit Binary Sum of The Following: 01000111 10000110

How to Calculate 8-bit Binary Sum

Adding two 8-bit binary numbers involves performing binary addition with each bit position, including any carry-over values. Here's how to do it:

1. Write both binary numbers vertically, aligning the least significant bits (rightmost) under each other.
2. Add the bits from right to left, one column at a time.
3. For each column, apply the binary addition rules:
   • 0 + 0 = 0
   • 0 + 1 = 1
   • 1 + 0 = 1
   • 1 + 1 = 10 (which is 0 with a carry of 1)
4. If there's a carry after the last column, it becomes the most significant bit (leftmost) of the result.
5. The result must be an 8-bit number, so any overflow beyond 8 bits is discarded.

Step-by-Step Calculation

Let's calculate the sum of 01000111 and 10000110 step by step:

1. Write the numbers vertically:

     01000111
   + 10000110
   

2. Add each column from right to left:
   • Rightmost column (bit 0): 1 + 0 = 1
   • Next column (bit 1): 1 + 1 = 10 → write 0, carry 1
   • Next column (bit 2): 1 + 1 + carry 1 = 11 → write 1, carry 1
   • Next column (bit 3): 0 + 0 + carry 1 = 1
   • Next column (bit 4): 0 + 0 = 0
   • Next column (bit 5): 0 + 0 = 0
   • Next column (bit 6): 1 + 1 = 10 → write 0, carry 1
   • Leftmost column (bit 7): 0 + 1 + carry 1 = 10 → write 0, carry 1 (overflow)
3. Combine the results: 01000111 + 10000110 = 11001101 (with overflow)
4. Since we're working with 8-bit numbers, we discard the overflow and keep 11001101.

Worked Example

Let's verify the calculation with another example: 01101010 + 00110110

1. Write the numbers vertically:

     01101010
   + 00110110
   

2. Add each column:
   • Bit 0: 0 + 0 = 0
   • Bit 1: 1 + 1 = 10 → write 0, carry 1
   • Bit 2: 0 + 1 + carry 1 = 10 → write 0, carry 1
   • Bit 3: 1 + 1 + carry 1 = 11 → write 1, carry 1
   • Bit 4: 0 + 0 + carry 1 = 1
   • Bit 5: 1 + 1 = 10 → write 0, carry 1
   • Bit 6: 1 + 0 + carry 1 = 10 → write 0, carry 1
   • Bit 7: 0 + 0 + carry 1 = 1
3. Combine the results: 01101010 + 00110110 = 10011100

The result is 10011100, which confirms our method works correctly.