Equivalent of the decimal number \( (25.375)_{10} \) in binary form
Equivalent of the decimal number \( (25.375)_{10} \) in binary form
Show Hint
- \( (11001.011)_2 \)
- \( (11101.011)_2 \)
- \( (11011.111)_2 \)
- \( (11001.101)_2 \)
The Correct Option is A
Solution and Explanation
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) \( (11001.011)_2 \).
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