Answer:
10010110 . 100011₂
Explanation:
A real number consists of two parts.
That is, ( 1 ) Integer part ( 2 ) fractional part
Let us take the given number as an example.
Here, 150 . 55 ← fractional part
↑
(integer part)
So, to make such a decimal number into a binary number you have to use a method like this.
- First, you have to make the integer part a binary number.
- For that, you have to divide the integer part by 2 until it gets zero.
- Important thing is you have to write the remainders in each step.
- After that, you have to write the remainders from bottom to top.
- Now, let us consider the fractional part.
- To convert the fractional part into a binary number you have to multiply only the fractional part in each step by two.
- There you'll get an integer part before the fractional part. In this step, you have to write the integer part from top to bottom.
Let us solve it now.
Integer part
2 |150
2 |75 - 0
2 | 37 - 1
2 | 18 - 1
2 | 9 - 0
2 | 4 - 1
2 | 2 - 0
2 | 1 - 0
0 - 1
∴ 150 ⇒ 10010110₂
Fractional part
| . 55 × 2
1 | . 10 × 2
0 | . 2 × 2
0 | . 4 × 2
0 | . 8 × 2
1 | . 6 × 2
1 | . 2
As this fractional part not getting the zero even we multiply by 2 continuously, we have to write an approximate value for this.
150.55 ⇒ 10010110 . 100011₂