Calculate The 8-Bit Binary Sum of The Following: 00000011 01101010

How to Calculate 8-bit Binary Sum

Adding two 8-bit binary numbers follows the same principles as decimal addition but with binary digits (bits) that can only be 0 or 1. Here's how the process works:

Binary Addition Rules

When adding two binary digits:

1. If both bits are 0, the result is 0
2. If one bit is 1 and the other is 0, the result is 1
3. If both bits are 1, the result is 0 and you carry over 1 to the next higher bit

8-bit Binary Addition

When working with 8-bit numbers, you're dealing with numbers that can be represented with 8 bits, from 00000000 to 11111111. The addition process is the same as with smaller binary numbers, but you have more bits to work with.

Step-by-Step Calculation

Let's calculate the sum of 00000011 and 01101010 step by step:

1. Write the numbers vertically, aligning the least significant bits:

   00000011
   01101010
   

2. Add the bits from right to left, starting with the least significant bit (rightmost):
   • Bit 1 (rightmost): 1 + 0 = 1
   • Bit 2: 1 + 1 = 10 (write down 0, carry over 1)
   • Bit 3: 0 + 0 + carry 1 = 1
   • Bit 4: 0 + 1 = 1
   • Bit 5: 0 + 0 = 0
   • Bit 6: 0 + 1 = 1
   • Bit 7: 0 + 0 = 0
   • Bit 8 (leftmost): 0 + 0 = 0
3. Combine the results from each bit position:

     00000011
   + 01101010
   -----------
     01101101
   

The final sum is 01101101.

Worked Example

Let's look at another example to reinforce the concept. Calculate the sum of 00001010 and 00001101:

1. Align the numbers:

   00001010
   00001101
   

2. Add the bits:
   • Bit 1: 0 + 1 = 1
   • Bit 2: 1 + 0 = 1
   • Bit 3: 0 + 1 = 1
   • Bit 4: 1 + 1 = 10 (write down 0, carry over 1)
   • Bit 5: 0 + 0 + carry 1 = 1
   • Bit 6-8: 0 + 0 = 0
3. Combine the results:

     00001010
   + 00001101
   -----------
     00010111
   

The sum is 00010111.