Floating Point Representation: Example

[michi155]

thx for the video, helped me more to understand 754

[shebotnov]

why use 3 bits for the mantissa, if singe has 23 bits and double as 52 bits for mantissa? You can at least use 4 hex for the mantissa if doing it manually

[numericalmethodsguy]

@shebotnov It is a hypothetical example to keep everything simple to explain. See all videos in the playlist of floating point representation.

[highsense100]

there are the some numbrs such as 0.9, 0.65 etc in which there may have infinite value so we just take first four values.

[Petahx3]

Decent explanation of the content.Could have used video editing or retake to correct the errors.

[amundead]

how can u get (0.9) 10 =0.111000?

A.S.A.P reply please. i got exam tomorrow

[ivXtreme]

Thanks man! I love how you provide a DETAILED example, unlike some teachers which assume the students will somehow magically figure out what they're doing on the board.

[hacksign000]

thank you so much, i understand it better now .

[yangxingyge]

1,The second comment is wrong(The integer bit "1" before the decimal point is hiddenly exist when exponent is not zero); 2.the exponent has no Sign bit(instead is bias).

一、第二个解释是错误的（小数点前的“1”位是默认存在的的）；

二、阶码没有符号。

[numericalmethodsguy]

@yangxingyge I do not understand the comment.  The example does not follow the IEEE-754 type of specification. We do that in a later example. See "floating point representation" playlist at the numericalmethodsguy channel. See last two videos.

[taostoner1]

@yangxingyge He mentioned that the exponent has no sign bit and bias was used instead. This was just an illustrative example.

[TheLole2009]

What happens if a binary number is given that starts with 0, for example 0.0010101 and to convert it into floating point. Do we move the dot to the right until we get to the first 1 bit or there is another way of calculating? By the way the video was very helpful

[numericalmethodsguy]

@TheLole2009 For a binary number such as you wrote 0.0010101, it would be written in floating format as 1.0101*2^(-3). The exponent hence would be (-11) in base 2 and the mantissa as 0101.

[TheLole2009]

@numericalmethodsguy

Thanks very much for the reply. It helped me with my assignment. You are much better than my teacher.

[wendy2212]

There isn't enough bits to represent the 0.9 portion of the number. Your answer would be the same if it were simply -13 as opposed to -13.9.

[numericalmethodsguy]

@wendy2212 You are right. It just goes to show that floating pt representation is an approximate representation of a number. You can repeat the exercise with more bits for the mantissa and exponent if you like!

[recharged01]

Life saver right here! I have a midterm in an hour

[TomaCukor]

@recharged01 so how'd it work out ?

[RajeevID]

Thank you

[gatnu3010]

Thank you for this video and the base conversion, it was really helpful.

[numericalmethodsguy]

Can you point the mistake to me?

[RuyABC]

Good materia. Its essential in computer science.

The Brazil express gratitude.

[videos12344444444]

confuse oO. Im really dont understand the base of conversion on float point oO...

[Terry1212]

Thanks for the video. Btw, the dog ate my homework. :D

[mosgba]

i got the 13 but not the 0.9 plz help me

[blitz0623]

0.9:

0.9 x 2 = 1.8. Use the 1. (1)

0.8 x 2 = 1.6. Use the 1. (11)

0.6 x 2 = 1.2. Use the 1. (111)

0.2 x 2 = 0.4. Use the 0. (1110)

0.4 x 2 = 0.8. Use the 0. (11100)

0.8 x 2 = back to 2nd operation. So the binary representation of 0.9 is:

11100 1100 1100 1100 etc. We just need the important bits, 11100.

[mosgba]

the actual reason am watching he put it to home work. oh no!

[mosgba]

thanx for helping i got it

[TheDesiretolearn]

In binary representation 9 is 1001. Isn't it?

[numericalmethodsguy]

It is the respresentation of 0.9. See this video youtube(dot)com/watch?v=96MJVz­VKoIE

[LoboLoko007]

I have just been studying binary and hexadecimals and I can surly say that... yes

1001(binary) is the equibalent of 9 (in decimals)

[Akillarian]

Thanks for the video. It's very helpful.

[Valefarous]

Thank you for this video! I've been struggling through a very dense chapter on fp representation that used a lot of heavy language from abstract algebra; this made it much clearer to me:)

[naco1020]

thank for the correction... :-)

[amightyo]

the mantissa is 101.

Thanks for the info...very useful.

[numericalmethodsguy]

Thank you for the correction. It has been annotated on the video. I hope to replace this part of the video later by re-taping it.