How to remove the unwanted zero at the end in the floating point variable?

Hello,

I have a floating point variable that I need to convert into into the binary.

So, at first i want to limit the number the digit after the decimal. To do that I am using output=round(input,4).

But after this, i get some unwanted zero that I do not want.

For example:

a=1.006600000000000 but I want only 1.0066

b=round(a,4) % the output is still 1.006600000000000

And then I want to convert it to binary (only 1.0066 to binary). How can I do that?

Please help

Thank you..

Answer 1

[Stephen23]

"How to remove the unwanted zero at the end in the floating point variable?"

Trailing zeros are just an artifact of displaying a specific binary value as a decimal number at a specific precision.

" a=1.006600000000000 but I want only 1.0066"

Binary floating point numbers do not store any information about how many decimal digits you want. Their precision is fixed to some number of binary digits, which cannot be changed. Both of your numbers are exactly the same:

a = 1.006600000000000;
b = 1.0066;
isequal(a,b)

ans = logical
   1

When you round to some (decimal) magnitude, you might get the same number or a slightly different number, it really does not make much difference in this case because both of them will display as the same value anyway:

b = round(a,4)

b = 1.0066

isequal(a,b)

ans = logical
   1

b+100*eps() % a slightly different number displays the same

ans = 1.0066

If you are interested you can display the exact decimal value of any binary floating point number by downloading this FEX submission:

https://www.mathworks.com/matlabcentral/fileexchange/22239-num2strexact-exact-version-of-num2str

or view the HEX of the binary floating point (note they are exactly the same):

num2hex(a)

ans = '3ff01b089a027525'

num2hex(b)

ans = '3ff01b089a027525'

Summary: how numbers are displayed is not the same thing as how they are stored in memory. Do not confuse the storage of a number with its representation when displayed with a specific format:

https://www.mathworks.com/help/matlab/ref/format.html

If you want to convert to binary you need to specify if you mean:

• a number written in base 2
• some kind of encoded number (e.g. binary floating point)

Which do you want?

Answer 2

[Walter Roberson]

And then I want to convert it to binary (only 1.0066 to binary). How can I do that?

a=1.006600000000000

a = 1.0066

bin = int16(a*2^14)

bin = int16 16492

restored_a = double(bin) / 2^14

restored_a = 1.0066

restored_a - a

ans = -8.2031e-06

Close enough for rock and roll.

The above handles values in the range -2 (exactly) to 1.99993896484375 . To handle larger ranges you either have to give up negatives, or give up decimal places (current precision is 0.00006103515625), or use more bits.