To convert the decimal number 1024 into its hexadecimal equivalent, we will follow a systematic approach. Let's break down the process step-by-step. Step 1: Understanding Decimal and Hexadecimal

• Decimal is a base-10 number system, which uses digits from 0 to 9.
• Hexadecimal is a base-16 number system, which uses digits from 0 to 9 and letters A to F (where A=10, B=11, C=12, D=13, E=14, F=15).

Step 2: Converting Decimal to Hexadecimal To convert a decimal number to hexadecimal, we can use the method of repeated division by 16. Here’s how it works:

1. Divide the decimal number by 16.
2. Record the quotient and the remainder.
3. Continue dividing the quotient by 16 until the quotient is 0.
4. The hexadecimal number is formed by the remainders, read in reverse order (from last to first).

Step 3: Performing the Conversion Let’s convert 1024 to hexadecimal:

1. First Division:
2. 1024 ÷ 16 = 64
3. Remainder = 1024 - (64 * 16) = 1024 - 1024 = 0
4. Second Division:
5. 64 ÷ 16 = 4
6. Remainder = 64 - (4 * 16) = 64 - 64 = 0
7. Third Division:
8. 4 ÷ 16 = 0
9. Remainder = 4 - (0 * 16) = 4

Now we have our remainders: - From the last division to the first, we have: 4, 0, 0. Step 4: Constructing the Hexadecimal Number Reading the remainders from last to first gives us: - The hexadecimal equivalent of 1024 is 400. Conclusion Thus, the correct answer is B. 400. Explanation of Other Options

• A. 24: This is incorrect because 24 in decimal is 36 in hexadecimal, which is far less than 1024.
• C. 3E8: This is incorrect because 3E8 in hexadecimal equals 1000 in decimal (3 * 256 + 14 * 16 + 8 * 1 = 768 + 224 + 8 = 1000).
• D. 8BB: This is incorrect because 8BB in hexadecimal equals 2235 in decimal (8 * 256 + 11 * 16 + 11 * 1 = 2048 + 176 + 11 = 2235).

Revision Summary

• Decimal to hexadecimal conversion involves repeated division by 16.
• The hexadecimal number is formed by reading the remainders in reverse order.
• The decimal number 1024 converts to hexadecimal as 400.
• Always check the other options to ensure they do not match the decimal equivalent of the given number.