To convert the hexadecimal number 4B7 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, where: - A = 10 - B = 11 - C = 12 - D = 13 - E = 14 - F = 15 Each hexadecimal digit can be directly converted to a 4-bit binary equivalent. This is because (2^4 = 16), meaning each hex digit corresponds to a unique 4-bit binary number. Step 2: Convert Each Hexadecimal Digit to Binary Now, let's convert each digit of 4B7 to its binary equivalent:

1. 4 in hexadecimal:
2. Decimal equivalent: 4
3. Binary equivalent: 0100
4. B in hexadecimal:
5. Decimal equivalent: 11
6. Binary equivalent: 1011
7. 7 in hexadecimal:
8. Decimal equivalent: 7
9. Binary equivalent: 0111

Step 3: Combine the Binary Equivalents Now, we combine the binary equivalents of each digit: - 4 → 0100 - B → 1011 - 7 → 0111 Putting them together, we get: - 4B7 in binary = 0100 1011 0111 Step 4: Remove Spaces For the final binary representation, we typically write it without spaces: - Final binary representation: 010010110111 Step 5: Identify the Correct Option Now, let's compare our result with the provided options: - A. 010010100111 - B. 010010110111 - C. 010010000111 - D. 010011000111 The correct answer is B. 010010110111. Explanation of Incorrect Options

• Option A (010010100111): This binary number has the second group of bits (after the first four) incorrect. The second group should be 1011 (for B), but it shows 1001 instead.
• Option C (010010000111): This option has the first group correct (0100 for 4) but incorrectly represents B as 0000 instead of 1011. The last group is correct (0111 for 7), but the overall binary number is incorrect.
• Option D (010011000111): This option incorrectly represents the first group as 0100 (which is correct) but changes the second group to 1100 instead of 1011. The last group is correct, but the overall binary number is incorrect.

Summary

• Each hexadecimal digit converts to a 4-bit binary number.
• The conversion for 4B7 is done digit by digit: 4 → 0100, B → 1011, 7 → 0111.
• The combined binary representation is 010010110111.
• The correct answer is B. 010010110111.

Revision Summary

• Hexadecimal digits convert to binary using 4 bits each.
• 4B7 in hexadecimal converts to binary as follows: 4 = 0100, B = 1011, 7 = 0111.
• The final binary representation is 010010110111.
• The correct option is B, as it matches the calculated binary value.