To convert the hexadecimal number 4B7(_{16}) to binary, we need to follow a systematic approach. Let's break it down step-by-step. Step 1: Understand Hexadecimal to Binary Conversion Hexadecimal (base 16) uses the digits 0-9 and the letters A-F to represent values. Each hexadecimal digit can be directly converted to a 4-bit binary number (since (2^4 = 16)). Step 2: Convert Each Hexadecimal Digit to Binary We will convert each digit of 4B7(_{16}) to its binary equivalent:

• 4 in hexadecimal is 0100 in binary.
• B in hexadecimal (which represents 11 in decimal) is 1011 in binary.
• 7 in hexadecimal is 0111 in binary.

Step 3: Combine the Binary Values Now, we combine the binary representations of each digit:

• For 4: 0100
• For B: 1011
• For 7: 0111

Putting these together, we get: [ 4B7_{16} = 0100 \, 1011 \, 0111 ] Final Answer Thus, the binary representation of 4B7(_{16}) is 0100 1011 0111. Correct Option The correct option is B: 0100 1011 0111. Explanation of Other Options

• Option A: 0100 1010 0111
• This option incorrectly converts the digit B. Instead of 1011, it uses 1010, which represents 10 in decimal, not 11.
• Option C: 0100 1000 0111
• This option incorrectly converts the digit B as well. It uses 1000, which represents 8 in decimal, not 11.
• Option D: 0100 1100 0111
• This option also incorrectly converts the digit B. It uses 1100, which represents 12 in decimal, not 11.

Common Pitfalls

• Misremembering Hexadecimal Values: It's crucial to remember the correct binary values for hexadecimal digits, especially for A-F.
• Forgetting to Use 4 Bits: Each hexadecimal digit must be represented by exactly 4 bits. Omitting leading zeros can lead to incorrect binary representations.

Revision Summary

• Each hexadecimal digit converts to a 4-bit binary number.
• 4B7(_{16}) converts to binary as follows: 4 = 0100, B = 1011, 7 = 0111.
• The combined binary representation is 0100 1011 0111.
• The correct answer is option B: 0100 1011 0111.