Question

can someone please tell me that what is dyadic expansion?

Answer 1

Google says it's simply the binary form of a number. Are you familiar with the binary number system? Base 2?

Answer 2

NO

Answer 3

Okay, well let me describe binary to you briefly.

Answer 4

YES PLEASE

Answer 5

Binary Numbers are expressed with digits 0 and 1.

Answer 6

If a binary number is 100100, then it is 1 * 2^3 + 1 * 2^6

Answer 7

That means, 8 + 64 = 70

Answer 8

oops, I meant 100100 = 1 * 2^2 + 2^5

Answer 9

4 + 32

Answer 10

Basically, in our number system, we have 10 symbols that we use to represent all of our numbers. 0,1,2,3,4,5,6,7,8, and 9. This is called base 10. And consider counting up from 0.
0, 1, 2... 8, 9
what do we do when we run out of symbols? Well, we add a "place value." 10. So, the first place value reset to 0, the lowest number, and we added a second place value that is worth 10 of the first.

Counting in binary works the same way, but we have to reset much more often because we only have two symbols.
0
1
10
11
100
101
110
111
1000
like that

Answer 11

actually I have the same question that someone posted at http://math.stackexchange.com/questions/117490/dyadic-expansion-proof but I don't understand the answer

Answer 12

That is counting in binary, starting with 0 and counting up to 8. Do you see what 9 would be? 10? 11?

Answer 13

Well, unfortunately I don't have time to try to wrap my head around or explain this proof right now. Sorry. That's dyadic expansions though. They happen to be using it for fractional numbers though.