![]() In this case it is 0 so we’ve got as far as 0.125 10 = 0.0? 2 We then take the whole number part of the result as the first binary digit after the radix point. To begin with we take the decimal fraction and multiply it by two (i.e. Next we need to deal with the fractional part of our decimal number (which as a reminder is 0.125).Īgain, there is a simple step-by-step method for performing the conversion. With the 1’s column, the value of the column (1 10) does actually fit into our reminder (1 10) so we put a 1 in that column and again subtract the value of the column (1 10) from our remainder (1 10) to get a new remainder (0 10). We then look at the 2’s column and again the value of that column (2 10) doesn’t fit into our remainder (1 10) so again we put a 0 in that column. It doesn’t, so we put a 0 in that column. We then look at the 4’s column and see if that fits into our remainder. If we look through the different binary number columns above we can see that the highest factor that fits would be 8 (or 2 3) so we put a 1 in the 8’s column and subtract the value of that column (8 10) from our original number (9 10) and make a note of the reminder (1 10). Step one is to find the highest factor of 2 that will fit into the integer part of our number. This time we’re going to use 9.125 10 and again deal with the left-hand side of the radix point first. Now what if we wanted to go the other way, from decimal to binary? I this next example, we’re going to take a decimal fraction and find it’s binary equivalent. Converting from a Decimal Fraction to a Binary Fraction So we have a fractional part that represents 0.625 10.Īll we have to do now is to combine the integer part and fractional parts together on either side of the radix point. Next, lets look at the right-hand side of the radix point. When looking at converting the binary on the left-hand side of the radix point we convert it just as we would when converting any binary integer number into its decimal equivalent. To get started lets look at the left-hand side. The process of converting a binary fraction into its decimal equivalent is really two-fold and we’ll deal with the numbers the the left-hand and right-hand sides of the radix point separately. Converting a Binary Fraction into a Decimal Fraction Let’s see if we can now take our binary fraction and convert it into its decimal equivalent. Notice how the exponent turns negative to the right-hand side of the radix point just as it does with decimal. Well, we could first break it down into its constituent components as follows: Say we wanted to represent the binary fraction 101.101 2 in decimal. I’ll try and use that terminology as we move forwards. So although the term decimal point is correct (at least for decimal), the more accurate term to use is the radix point ( ). Well, as I’ve mentioned previously, an alternative name for the number base of a particular notation is the radix. In this next example though we’re not representing numbers as decimal, we’re going to be using binary, so what do we call this separator? In the description I gave above, I called the separator between the integer and fractional parts of the number the decimal point. The first thing to mention here is that we need to correct some terminology. So given this, lets take a look at a similar example in binary. (As a side note, for those who are a bit rusty with their maths remember that 10 -n is exactly the same as writing 1/10 n). What you might not have realised is that just as the exponent (the number by which our number base or radix is raised) is reduced by one as we moved from left to right toward the decimal point, that trend continues on the right-hand side of the decimal point.Īs our exponent becomes negative we get fractions and in the case of decimal this results in the 10ths, 100ths, 1000ths columns and so forth. As you can see the fractional part is also made up of a number of different columns representing fractional components of different sizes. In this case though, on the right hand side of the decimal point we also have our fractional parts. As we saw with integer numbers, we have different columns on the left hand side of the decimal point that represent different components of the integer part of our number.
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