Adding Binary Fractions: A Simple Guide to Calculating and Understanding Results

In summary, when adding numbers in binary, you first add the digits in each position and carry over any excess to the next position. This works for any base, including binary, decimal, and hexadecimal. So, 0.1 + 0.1 = 1.0 in binary, just like 0.9 + 0.3 = 1.2 in binary. This is due to the way our number system is designed to handle overflow.
  • #1
soonsoon88
54
0
10.00 + 00.11 = 10.11 ...am i right?

how about if..
0.1 + 0.1 = ?
is it equal to 1.0 ?

thx for helping =)
 
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  • #2
Yep, it works just like in "ordinary" fractions.

If you want to add 0.9 and 0.3, you first add 9 and 2 giving 12. So you write down 2 and carry 1 to the next position, giving 0 + 0 + 1 = 1. Therefore, 0.9 + 0.3 = 1.2

Similarly, if you want to add 0.1 and 0.1, you first do 1 + 1 = 10, so you write down 0 and carry 1 to the next position, giving 0 + 0 = 1. Therefore, 0.1 + 0.1 = 1.0.
Indeed, 0.1 in binary corresponds to 0.5 in decimal notation, and 0.5 + 0.5 = 1.0 which is also 1.0 in binary notation.

All this works for any base, in fact. For example, in a hexadecimal base, 0.a3 + 0.63 = 1.06, because 3 + 3 = 6 (write 6, carry 0); a + 6 + 0 = 10 (write 0, carry 1) and 0 + 0 + 1 = 1. This is sort of by definition of our system to write down numbers, in which any "overflow" of one position counter is automatically "caught" by the next one (i.e. if the units counter overflows then we start adding to the tens-counter).
 
  • #3


I would like to clarify that adding binary fractions follows the same principles as adding decimal fractions. In the provided example, 10.00 + 00.11, the correct answer is indeed 10.11. This is because in binary, the number 1 represents the value of 2^0, while the number 0 represents the value of 2^-1. Therefore, 10.00 is equivalent to 2^1 + 0 x 2^0 + 0 x 2^-1 + 0 x 2^-2, which simplifies to 2. Similarly, 00.11 is equivalent to 0 x 2^1 + 0 x 2^0 + 1 x 2^-1 + 1 x 2^-2, which simplifies to 0.75. When we add these two together, we get 2.75, which is equivalent to 10.11 in binary.

In regards to the second question, 0.1 in binary is equivalent to 0.5 in decimal, and when we add two 0.1's together, we get 1.0 in binary, which is equivalent to 1 in decimal. So, the answer is yes, 0.1 + 0.1 = 1.0 in binary. I hope this clarifies any confusion and helps with your understanding. Thank you for asking and seeking clarification.
 

1. What are binary fractions?

Binary fractions are numbers represented in the base-2 numbering system, where each digit can only have a value of 0 or 1. They are used in computer programming to represent numbers and perform calculations.

2. How do you add two binary fractions?

To add binary fractions, you first need to convert them to the same denominator. Then, you can add the numerators together and simplify the resulting fraction if necessary. Finally, you may need to convert the resulting fraction back to binary form.

3. What is the easiest way to add binary fractions?

The easiest way to add binary fractions is to use a calculator or a computer program. There are also certain rules and shortcuts that can make the process easier, such as adding the fractions vertically or carrying over any remainders from the previous addition.

4. Can you add more than two binary fractions at once?

Yes, you can add more than two binary fractions at once. The process is similar to adding two fractions, where you first convert them to a common denominator and then add the numerators together. You can continue this process for as many fractions as needed.

5. Are there any special considerations when adding binary fractions?

Yes, there are a few special considerations when adding binary fractions. One important consideration is to always check for overflow, which can occur when the resulting fraction has more digits than the original fractions. Additionally, it is important to be aware of any leading zeros in the binary fractions, as they may affect the final calculation.

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