How to Convert from Other Number Bases to Decimal System?

Questions on conversion of numbers in some base to some other base is very common in competitive examination. Here in this post I present a simple technique to help you do such conversions.

First, let us understand what do we mean by number bases or systems. In our decimal number system, the rightmost position represents the “ones” column, the next position represents the “tens” column, the next position represents “hundreds”, etc. Therefore, the number 123 represents 1 hundred and 2 tens and 3 ones, whereas the number 321 represents 3 hundreds and 2 tens and 1 one.

The values of each position correspond to powers of the base of the number system. So for our decimal number system, which uses base 10, the place values correspond to powers of 10:
… 1000    100       10           1

… 103        102      101         100 Read More

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How to convert from decimal to other number systems

This post will be of special interest for people who are regularly in touch with mathematics. Students preparing for competitive examinations usually have Base System (Number Systems) in the list of their topics under quantitative aptitude.

Conversion from decimal to binary and other number bases

In order to convert a decimal number into its representation in a different number base, we have to be able to express the number in terms of powers of the other base. For example, if we wish to convert the decimal number 100 to base 4, we must figure out how to express 100 as the sum of powers of 4.

100 = (1 x 64) + (2 x 16) + (1 x 4) + (0 x 1)

= (1 x 4^3) + (2 x 4^2) + (1 x 4^1) + (0 x 4^0)

Then we use the coefficients of the powers of 4 to form the number as represented in base 4: Read More

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