Question

What is the hexadecimal representation of the decimal number 265?

• A. 0x10001001
• B. 0x411
• C. 0x190
• D. 0x109

Hint:

To convert a decimal number to hexadecimal, first convert it to binary, then group the binary digits in sets of four and convert each group to its hexadecimal equivalent.

Answer 1

The Correct Option is D

Step 1: Convert the decimal number to binary. 
The decimal number 265 can be converted to binary as follows: \[ 265 \div 2 = 132 \, \text{remainder} \, 1 \\ 132 \div 2 = 66 \, \text{remainder} \, 0 \\ 66 \div 2 = 33 \, \text{remainder} \, 0 \\ 33 \div 2 = 16 \, \text{remainder} \, 1 \\ 16 \div 2 = 8 \, \text{remainder} \, 0 \\ 8 \div 2 = 4 \, \text{remainder} \, 0 \\ 4 \div 2 = 2 \, \text{remainder} \, 0 \\ 2 \div 2 = 1 \, \text{remainder} \, 0 \\ 1 \div 2 = 0 \, \text{remainder} \, 1 \] Thus, the binary representation of 265 is \( 100001001_2 \).

Step 2: Convert the binary number to hexadecimal. 
Group the binary digits into sets of four starting from the right: \[ 1000 \, 0100 \, 1 \Rightarrow 0001 \, 0001 \, 0001 \] So, the hexadecimal representation is \( 0x109 \).

Step 3: Conclusion. 
Thus, the correct hexadecimal representation of the decimal number 265 is \( 0x109 \), and the correct answer is (d).