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okay here's the problem:

*find fl(x) for 9.4*

and here's how it's done

9.4 in binary is 1001.0110 0110 0110 since

9 = 1001

.4 = .0110 0110 0110... (basically, 0110 repeating)

next using Rounding to Nearest Rule (see top on picture) we get what a binary number (boxed in black in the picture below)

I understand how to do upto here perfectly however I do not understand what happens after that.

I'm confused by pretty much the entire thing that follows after "discarding the infinite tail". I do not understand how fl(9.4) turns out to be 9.4 + 0.2 x 2^(-49) (shown in red box in the picture).

could anyone provide explanation for this?

the book has another example similar to this but i couldn't follow either of them. i hope someone can explain me the basics of what is happening here.

http://i.imgur.com/IOpfVjm.jpg

(image not embedded because it is too big and breaks the thread)

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# Could someone explain this textbook example regarding float fl(x)

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