Decimal to Binary,Octal and Hexadecimal

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         CONVERSION FROM DECIMAL TO BINARY, OCTAL, HEXADECIMAL

A decimal number has two parts—integer part and fraction part. For example, in the decimal number 23.0786, 23 is the integer part and .0786 is the fraction part. The method used for the conversion of the integer part of a decimal number is different from the one used for the fraction part. In the following subsections, we shall discuss the conversion of decimal integer, decimal fraction and decimal integer.fraction number into binary, octal and hexadecimal number.

                  Converting Decimal Integer to Binary, Octal, Hexadecimal

A decimal integer is converted to any other base, by using the division operation. To convert a decimal integer to—
·         binary-divide by 2,
·         octal-divide by 8, and,
·         hexadecimal-divide by 16.

Let us now understand this conversion with the help of some examples.

Example 1: Convert 25 from Base 10 to Base 2.
1.        Make a table as shown below. Write the number in centre and toBase on the left side.

to Base Number      Remainder

(Quotient)
2           25

 2.        Divide the number with toBase. After each division, write the remainder on right-side column and quotient in the next line in the middle column. Continue dividing till the quotient is 0.
         

to Base Number    Remainder

(Quotient)


2
25

2
12
1
2
6
0
2
3
0
2
1
1

0
1
3.        Write the digits in remainder column starting from downwards to upwards,













The binary equivalent of number (25)10 is (11001)2

The steps shown above are followed to convert a decimal integer to a number in any other base.

 Example 2: Convert 23 from Base 10 to Base 2, 8, 16.


 Example 3: Convert 147 from Base 10 to Base 2, 8 and 16.


Example 4: Convert 94 from Base 10 to Base 2, 8 and 16.

                 

            Converting Decimal Fraction to Binary, Octal, Hexadecimal

A fractional number is a number less than 1. It may be .5, .00453, .564, etc. We use the multiplication operation to convert decimal fraction to any other base.

To convert a decimal fraction to—

·         binary-multiply by 2,
·         octal-multiply by 8, and,
·         hexadecimal-multiply by 16.

Steps for conversion of a decimal fraction to any other base are—

1.        Multiply the fractional number with the to Base, to get a resulting number.
2.        The resulting number has two parts, non-fractional part and fractional part.
3.        Record the non-fractional part of the resulting number.
4.        Repeat the above steps at least four times.
5.        Write the digits in the non-fractional part starting from upwards to downwards.


Example 5: Convert 0.2345 from Base 10 to Base 2.

The binary equivalent of (0.2345)10 is (0.001111)2

 Converting Decimal Integer.Fraction to Binary, Octal, Hexadecimal

Example 6: Convert 34.4674 from Base 10 to Base 2.


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