Answer:
The binary equivalent of the decimal number 38.37510 is 100110.0112. Therefore, the correct option is: 100110.011
Explanation:
To convert the decimal number 38.375 to binary, we can convert the integer part (38) and the fractional part (0.375) separately and combine them.
For the integer part:
38 divided by 2 gives a quotient of 19 with a remainder of 0.
19 divided by 2 gives a quotient of 9 with a remainder of 1.
9 divided by 2 gives a quotient of 4 with a remainder of 1.
4 divided by 2 gives a quotient of 2 with a remainder of 0.
2 divided by 2 gives a quotient of 1 with a remainder of 0.
1 divided by 2 gives a quotient of 0 with a remainder of 1.
Reading the remainders from bottom to top gives the binary equivalent of the integer part: 1001102.
For the fractional part:
0.375 multiplied by 2 gives a product of 0.75, and the whole number part is 0.
0.75 multiplied by 2 gives a product of 1.5, and the whole number part is 1.
0.5 multiplied by 2 gives a product of 1, and the whole number part is 1.
Continuing this process until we get a fraction of 0 or reach the desired precision gives the binary equivalent of the fractional part: 0.0112.
Combining the two parts, we get the binary equivalent of the decimal number 38.37510: 100110.0112.
The reason is that to convert a decimal number to binary, we need to represent both the integer part and fractional part in binary separately, and then concatenate them to get the final binary representation.
So, to convert the decimal number 38.37510 to binary, we first convert the integer part, which is 38, to binary using the division-by-2 method as explained in the previous answer. This gives us 100110 in binary.
Next, we convert the fractional part, which is 0.375, to binary using the multiplication-by-2 method as explained in the previous answer. This gives us 0.011 in binary.
We then concatenate the two binary values to get the final binary representation of 38.37510, which is 100110.0112.
Therefore, the correct option is 100110.011.