And maximum possible conversion error, in that case, is one-half of it, or 0.0078125. The value of the rightmost digit is called resolution or precision and defines the smallest possible nonzero number, which can be written using this number of digits. And this is our error during conversion decimal 0.8 to binary with 6 digits after the point. But it is not decimal 0.8 in fact, but it is decimal 0.796875 the difference is that it is 0.003125. For example, let's convert decimal 0.8 to binary and use 6 digits after the point. The error depends on the number of digits after the point which we decide to use. That's why the conversion of fractional numbers often gives us conversion error. In fact, it is a periodic number with period 1100, so we won't find the exact number of binary digits to write 0.8 precisely. We can go on, but even now, we can see that decimal 0.8 is binary 0.11001100.(and many digits). But for the binary numeral system, we have problems. Take a look at decimal number 0.8Įverything is easy for the decimal numeral system.
Since we have fractions and denominators that are different, we can't always keep the same precision with varying numerals systems.Īgain, let me show it with an example. Wasn't that easy?īut, there is one caveat. Let's take, for example, infamous binary system, and fractional binary number 110.001. After Ive made several calculators for numeral systems conversion (from the simplest one to more advanced: Conversion of decimal number to other notations, Conversion from decimal numeral system, Conversion between any. You can write it like this:Įasy to follow, isn't it? But it is the same thing for any other positional numeral system. This online calculator helps to convert fractional number in one numeral system to fractional number in other numeral system. All we need to remember is that we deal with the positional numeral system. So, I used to think that converting fractional numbers is difficult, but it turns out to be relatively easy to understand.
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