Floating Point Representation: Example

Learn via an example of how a number in base-10 is represented as floating point number in base-2.

Category:

Education

Tags:

• floating
• point
• representation
• binary
• number
• numerical
• methods
• numericalmethodsguy

[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.

[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.

[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.

[Terry1212]

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

[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.

[michi155]

thx for the video, helped me more to understand 754

[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

[taostoner1]

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

[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 .