How do I convert a decimal fraction into binary fraction?

[alangs]

How do I convert the decimal fraction (0.859375)10 into a binary fraction???

 

[keith1200rs]

0.859375 isn't a fraction. There is an example of conversions for numbers less than unity here:

**broken link removed**

Keith.

 

[_Eduardo_]

Multiply by 2 as the link above.


But 0.859375 = 55/64 then just shift right 55 binary 6 times.

0.859375 = 0.110111

 

[Girly_girl]

how would you do this in Matlab?

 

[Kral]

An easy way is to convert to hex first and then convert hex to binary.
Multiply by 16
write down the integer portion in hex (12 = C, 14 = E, etc)
subtract the integer portion from the result
multiply by 16
write down the integer portion in hex
continue until the fractional portion = zero, or you have enough accuracy.
For your example:
.859375 X 16 = 13.75 (Write down "D")
13.75 -13 = .75
.75 X 16 = 12 Write down "C")
The fractional part is now zero, so you're done
The answer in hex is DC = 11011100 binary

If you have a scientific calculator with a "Hex" mode, and you are satisfied with 4 hex digits of accuracy, do the following:
In decimal mode, multiply the fraction by 65536.
.859375 X 65536 = 56320
Switch to "Hex" mode.
DC00 is displayed.
.
Remember, if you are using twos complement representation, the binary result must be shifted right 1 place to make room for the sign bit.
Regards,
Kral