Question

What is the binary equivalent of the decimal number 25?

• A. 11001
• B. 10101
• C. 11101
• D. 10011

Hint:

You can also build the number using powers of 2 (16, 8, 4, 2, 1). \(25 = 16 + 8 + 1\). Place a 1 under the used values and 0 otherwise to get 11001.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The task is to translate the base-10 decimal value 25 into its corresponding base-2 binary format.
Step 2: Key Formula or Approach:
Decimal to binary conversion involves continuously dividing the number by 2 and noting the remainders. The final binary string is formed by reading these remainders in reverse order (from the last quotient to the first).
Step 3: Detailed Explanation:
Executing the repeated division by 2 for 25 yields:
\[ 25 \div 2 = 12 \text{ (Remainder } 1) \] \[ 12 \div 2 = 6 \text{ (Remainder } 0) \] \[ 6 \div 2 = 3 \text{ (Remainder } 0) \] \[ 3 \div 2 = 1 \text{ (Remainder } 1) \] \[ 1 \div 2 = 0 \text{ (Remainder } 1) \] Collecting the remainders from the bottom up gives the sequence \(11001\).
Hence, the binary form of \(25_{10}\) is \(11001_{2}\).
Step 4: Final Answer:
The correct choice is (A).