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Convert Decimal to Binary and Octal

Complement of a Number   Number System   Types of Number system

In our previous article, we had discussed Convert any number into Decimal Number. Now, In this article we can easily understand how to convert Decimal Number into other Number

Note : The Rule is very simple. Any number which you want convert Decimal to required format. Just divide by its base to this number and remainder is taken from bottom to top. Let’s understand with some examples

Convert Decimal to Binary

Ex 1. Convert (41)10 into Binary Number

Sol. 41 is divide by 2 because the base of binary number is 2

      Integer quotient   Quotient     Remainder

       41 / 2                      20                     1

       20 / 2                      10                     0

       10 / 2                      5                       0

       5 / 2                        2                       1

       2 / 2                        1                       0

       1 / 2                        0                       1

Remainder should be taken from bottom

The Answer is (101001)2

 

Ex2. Convert (153)10  into Octal Number

Sol. 153 is divided by 8 because the base of octal is 8.

      Integer quotient   Quotient     Remainder

      153 / 8                      19                     1

      19 / 8                         2                      3

      2 / 8                           0                      2

Remainder should be taken from bottom

The Answer is (231)8

Note: The above examples are of without decimal point. Now let’s discuss some examples with Decimal point. The rule is little bit different. In above examples, we have divided the numbers by its corresponding base, but if a number has decimal point, then after decimal point the number is multiplied by its base.  The number should be taken from Top to Bottom. Let’s understand with an example.

Ex 3. Convert (0.6875)10 into Binary Number

Sol. The number is multiplied by 2 because the base of binary number is 2

       Number                       Integer     fraction     cofficient

        0.6875 * 2 = 1.3750 =     1    +     0.3750           1

        0.3750 * 2 = 0.7500 =     0    +     0.7500           0

        0.7500 * 2 = 1.5000 =     1    +     0.5000           1

        0.5000 * 2 = 1.0000 =     1    +     0.0000           1

The Answer is (0.1011)2

Ex 4. Convert (0.513)10 into Octal Number

Sol. The number is multiplied by 8 because the base of binary number is 8

       Number                     Integer   fraction   cofficient

        0.513 * 8 = 4.104 =     4    +     0.104           4

        0.104 * 8 = 0.832 =     0    +     0.832           0

        0.832 * 8 = 6.656 =     6    +     0.656           6

        0.656 * 8 = 5.248 =     5    +     0.248           5

        0.248 * 8 = 1.984 =     1    +     0.984           1

This is an infinite sequence because it is not ended at a certain position. Now we should stop them after some multiplications and answer should be written as

(0.40651….)8

The Conversion of decimal numbers with both integer and fraction parts is done by converting the integer and fraction separately and then combining the two answers together. Using the results of Example 1 and 3

(41.6875)10 = (101001.1011)2

From Examples 2 and 4, we have

(153.513)10 = (231.206517)8

From above examples it is cleared that we can solve the decimal number, by solving integer and fractional part separately and at last we should merge them to get final answer.

Exercise:

Convert the following Decimal Number

1.       Convert (8702)10 to Binary

2.       Convert (99852.5)10 to Binary

3.       Convert (654)10 to Octal

4.       Convert (1150.51)10 to Octal

5.       Convert (1111)10 to Binary


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