Question:
Convert decimal number \(25\) into binary.
Convert decimal number \(25\) into binary.
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For decimal-to-binary conversion:
keep dividing by \(2\) until the quotient becomes \(0\), then read remainders upward.
Updated On: Jun 8, 2026
- \(11001\)
- \(10101\)
- \(11101\)
- \(10011\)
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The Correct Option is A
Solution and Explanation
Concept:
To convert a decimal number into binary, we repeatedly divide the number by \(2\) and record the remainders. The binary number is obtained by reading the remainders from bottom to top.
This method is called the repeated division method.
Step 1: Divide the decimal number by 2 repeatedly.
\[ 25 \div 2 = 12 \text{ remainder }1 \] \[ 12 \div 2 = 6 \text{ remainder }0 \] \[ 6 \div 2 = 3 \text{ remainder }0 \] \[ 3 \div 2 = 1 \text{ remainder }1 \] \[ 1 \div 2 = 0 \text{ remainder }1 \]
Step 2: Write the remainders from bottom to top.
\[ 11001 \]
Step 3: Verify the result.
\[ 1\times2^4+1\times2^3+0\times2^2+0\times2^1+1\times2^0 \] \[ =16+8+0+0+1 \] \[ =25 \] Hence the conversion is correct. \[ \boxed{11001} \]
Step 1: Divide the decimal number by 2 repeatedly.
\[ 25 \div 2 = 12 \text{ remainder }1 \] \[ 12 \div 2 = 6 \text{ remainder }0 \] \[ 6 \div 2 = 3 \text{ remainder }0 \] \[ 3 \div 2 = 1 \text{ remainder }1 \] \[ 1 \div 2 = 0 \text{ remainder }1 \]
Step 2: Write the remainders from bottom to top.
\[ 11001 \]
Step 3: Verify the result.
\[ 1\times2^4+1\times2^3+0\times2^2+0\times2^1+1\times2^0 \] \[ =16+8+0+0+1 \] \[ =25 \] Hence the conversion is correct. \[ \boxed{11001} \]
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