# Adding Binary Fractions

#### soonsoon88

10.00 + 00.11 = 10.11 ...am i right?

0.1 + 0.1 = ?
is it equal to 1.0 ?

thx for helping =)

#### CompuChip

Homework Helper
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).

### The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving