# Converting numbers (binary and so on)

Anyone can help me to solve the problem?

how to convert 0.65 (decimal numbers) to binary,octal and hexadecimal numbers?
thx..=)

OmCheeto
Gold Member
Anyone can help me to solve the problem?

how to convert 0.65 (decimal numbers) to binary,octal and hexadecimal numbers?
thx..=)

I would first convert 0.65 into a proper fraction of the lowest common denominator in base 10, convert the numerator and denominator to the new base, then do long division.

0.65 = 65/100 = 13/20 ----> 1101/101002 = 15/248 = D/1416

Of course, you have to know how to do long division in the different bases.

Here is a website that does it for you. http://www.easysurf.cc/cnver17.htm#b10tob2

Once you are done reading that, for Octal and Hex its exactly the same process except you multiply and divide by 8 and 16 instead of by 2.

After you've converted 0.65 to binary, there's a shortcut to convert it to octal and hex. Just group the bits into 3s (for octal) and 4s (for hex). For example, 0.101 would be 0.5 in octal and 0.A in hex.

By the way, you can also check your binary answer with the decimal/binary converter I wrote: http://www.exploringbinary.com/binary-converter/ . It is arbitrary precision, which means you can convert very large and very small numbers.

I would first convert 0.65 into a proper fraction of the lowest common denominator in base 10, convert the numerator and denominator to the new base, then do long division.

0.65 = 65/100 = 13/20 ----> 1101/101002 = 15/248 = D/1416

Of course, you have to know how to do long division in the different bases.

That would be the best way to do it in a computer, but I'd say the "repeated multiplication by new base" method works best for humans!