NIMCET 2023 — Computer PYQ

Conversion of Decimal to Binary 
The decimal number $(25.375{)}_{10}$ is converted to its binary equivalent by converting the integer part and the fractional part separately. 
Integer Part Conversion 

1. The integer part, $25$, is repeatedly divided by $2$, and the remainders are recorded. 
2. $25÷2=12$ with a remainder of $1$. 
3. $12÷2=6$ with a remainder of $0$. 
4. $6÷2=3$ with a remainder of $0$. 
5. $3÷2=1$ with a remainder of $1$. 
6. $1÷2=0$ with a remainder of $1$. 
7. The binary representation of the integer part is obtained by reading the remainders from bottom to top, resulting in $(11001{)}_2$. 

Fractional Part Conversion 

1. The fractional part, $0.375$, is repeatedly multiplied by $2$, and the integer part of the result is recorded. 
2. $0.375\times 2=0.75$, with an integer part of $0$. 
3. $0.75\times 2=1.50$, with an integer part of $1$. 
4. $0.50\times 2=1.00$, with an integer part of $1$. 
5. The binary representation of the fractional part is obtained by reading the integer parts from top to bottom, resulting in $(.011{)}_2$. 

Combining the Parts 

1. The binary equivalent of $(25.375{)}_{10}$ is formed by combining the binary representations of the integer and fractional parts, which is $(11001.011{)}_2$. 

Final Answer 
The final answer is $\boxed{\text{A}}$.