How many Kilobytes are there in a Megabyte?

Question

BlackTom AI · Accepted Answer

Using binary-based definitions common in computing: 1 kilobyte (KB) = 2^10 bytes = 1024 bytes, and 1 megabyte (MB) = 2^20 bytes = 1,048,576 bytes. Therefore a megabyte contains 1024 kilobytes.

1) Relevant knowledge points and concepts
- Byte: the basic unit of digital information (8 bits).
- Kilobyte (KB): commonly defined in computing as 2^10 bytes = 1024 bytes (binary prefix).
- Megabyte (MB): commonly defined in computing as 2^20 bytes = 1,048,576 bytes (binary prefix).
- Note: SI/decimal definitions sometimes use 1 KB = 1,000 bytes and 1 MB = 1,000,000 bytes, but computing conventions typically use powers of two (or use KiB/MiB for unambiguous binary units).

2) Complete reasoning process step by step
- Start from binary definitions: 1 KB = 2^10 bytes.
- 1 MB = 2^20 bytes.
- To find how many KB in 1 MB, divide bytes in 1 MB by bytes in 1 KB.

3) Calculations with intermediate steps
- 1 KB = 2^10 = 1,024 bytes.
- 1 MB = 2^20 = 1,048,576 bytes.
- Number of KB in 1 MB = (1,048,576 bytes) / (1,024 bytes per KB) = 1,048,576 / 1,024 = 1,024.
- Also using exponents: 2^20 / 2^10 = 2^(20−10) = 2^10 = 1024.

4) Why the correct answer is correct
- Because megabyte and kilobyte are defined as powers of two in computing, dividing 2^20 by 2^10 yields 2^10, which equals 1024. Thus there are 1024 KB in 1 MB.

5) Why the other options are incorrect
- a. 8: This is the number of bits in one byte, not KB per MB.
- b. 64: Equal to 2^6, not related to the KB→MB factor.
- d. 1000: Matches the decimal/SI convention (1 MB = 1,000 KB) used in some contexts, but not the conventional binary-based computing definition used in this question.

6) Conclusion
The correct choice is c. 1024, which matches the provided answer.

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