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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