CONVERSION AMONG RADICES
Convert from Decimal to Any Base
Let’s think about what you do to obtain each digit. As an example, let’s start with a decimal number 1234
and convert it to decimal notation. To extract the last digit, you move the decimal point digit, you move the decimal point left by one digit, which means you divide the given number by its base 10.
1234/10 = 123 + 4/10
To remainder of 4 is the last digit. To extract the next last digit, you again move the decimal point left by one digit and see what drops out.
123/10 = 12 + 3/10
The remainder of 3 is the next last digit. You repeat this process until there is nothing left. Then you stop in summary, you do the following:
Conclusion:
In conclusion, the easiest way to convert fixed point numbers to any base is to convert each part separately. We begin by separating the number into its integer and fractional part. The integer part is converted using the remainder method, by using a successive division of the number in the base until a zero is obtained. At each division, the reminder is kept and then the new number in the base r is obtained by reading the remainder from the last to remainder upwards.
The conversion of the fractional part can be obtained by successively multiplying the fraction with the
base. If we iterate this process on the remaining fraction, then we will obtain successive significant digit. This methods form the basis of the multiplication methods of converting fractions between bases.
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