Question

Equivalent of the decimal number \( (25.375)_{10} \) in binary form

• A. \( (11001.011)_2 \)
• B. \( (11101.011)_2 \)
• C. \( (11011.111)_2 \)
• D. \( (11001.101)_2 \)

Hint:

To convert a decimal number to binary, convert both the integer and fractional parts separately.

Answer 1

The Correct Option is A

Step 1: Convert the integer part \( 25 \) from decimal to binary: 
\[ 25 \div 2 = 12 \text{ remainder } 1 \\ 12 \div 2 = 6 \text{ remainder } 0 \\ 6 \div 2 = 3 \text{ remainder } 0 \\ 3 \div 2 = 1 \text{ remainder } 1 \\ 1 \div 2 = 0 \text{ remainder } 1 \] Thus, \( 25_{10} = 11001_2 \). 

Step 2: Convert the fractional part \( 0.375 \) from decimal to binary: 
\[ 0.375 \times 2 = 0.75 \text{ (integer part is 0)} \\ 0.75 \times 2 = 1.5 \text{ (integer part is 1)} \\ 0.5 \times 2 = 1.0 \text{ (integer part is 1)} \] Thus, \( 0.375_{10} = .011_2 \). 

Step 3: Combine the results: 
\[ 25.375_{10} = 11001.011_2 \] Thus, the correct answer is (a) \( (11001.011)_2 \).