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 question asks for the conversion of the base-10 decimal number 25 into its base-2 binary equivalent.


Step 2: Key Formula or Approach:
To convert a decimal number to binary, repeatedly divide the number by 2 and record the remainders. The binary representation is obtained by reading the remainders from bottom to top (from the last division to the first).


Step 3: Detailed Explanation:
Let us perform the repeated division by 2 for the number 25:
\[ 25 \div 2 = 12 \text{ with a remainder of } 1 \] \[ 12 \div 2 = 6 \text{ with a remainder of } 0 \] \[ 6 \div 2 = 3 \text{ with a remainder of } 0 \] \[ 3 \div 2 = 1 \text{ with a remainder of } 1 \] \[ 1 \div 2 = 0 \text{ with a remainder of } 1 \] Reading the remainders from the last division upwards (bottom to top), we get \(11001\).
Thus, the binary equivalent of \(25_{10}\) is \(11001_{2}\).


Step 4: Final Answer:
The correct choice is (A).