Binary Addition: How to Add Binary Numbers with Examples

In summary, binary addition is a mathematical operation used to add two binary numbers together, with a base of 2. It is necessary in digital electronics and computer science because computers use binary to process data. To add binary numbers, you start from the rightmost bit and work your way to the left, carrying over to the next column when the sum is greater than 1. An example of binary addition is adding 1011 and 1100, which results in 10111. The carryover rule in binary addition states that when adding two 1s, the result is 0 and a carryover of 1 to the next column, similar to the carryover rule in decimal addition.
  • #1
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Homework Statement


Shown is two binary numbers adding with the answer
binary.PNG


The Attempt at a Solution



Looking at the end side 1.1+1.1, shouldn't that be 11.00... instead of 10.00...
 

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  • #2
I agree, it should be 11...
 
  • #3
Yes, it should.
 

1. What is binary addition?

Binary addition is the process of adding two binary numbers together to get a sum. Binary numbers are numbers that are represented using only two digits, 0 and 1.

2. How do you add binary numbers?

To add binary numbers, you follow the same rules as adding decimal numbers. You start by adding the rightmost digits, and if the sum is greater than 1, you carry the 1 to the next column. You continue this process until you have added all the columns and have a final sum.

3. Can you provide an example of binary addition?

Sure, let's add 101 (5 in decimal) and 110 (6 in decimal).
  101
+ 110
 ---
  1011 (11 in decimal)

4. What happens when you add 1 and 1 in binary?

In binary, 1 + 1 equals 10. This is because in binary, you only have two digits, so when you add two 1s, it becomes 10. This is similar to how in decimal, when you add 9 + 1, it becomes 10.

5. Are there any special cases in binary addition?

Yes, when you add 0 and 0 in binary, the sum is also 0. This is because in binary, 0 + 0 = 0, just like in decimal. Additionally, when you add 1 and 0, the sum is 1, and when you add 0 and 1, the sum is also 1.

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