How many megabytes (MB = 2 to the power of 20 bytes) are in a terabyte
(1TB = 2 to the power of 40 bytes):
The Correct Answer and Explanation is:
To calculate how many megabytes (MB) are in a terabyte (TB), we need to understand the relationship between the different units of digital storage. In binary, each unit is based on powers of 2, which is commonly used in computing.
Understanding the Units
- Terabyte (TB):
- By definition, 1 terabyte (TB) is equal to ( 2^{40} ) bytes. This comes from the binary system, where each level is a power of 2.
- Megabyte (MB):
- Similarly, 1 megabyte (MB) is equal to ( 2^{20} ) bytes.
Step-by-Step Calculation:
To determine how many megabytes are in a terabyte, we divide the number of bytes in a terabyte by the number of bytes in a megabyte.
[
\text{Number of MB in 1 TB} = \frac{2^{40} \text{ bytes in 1 TB}}{2^{20} \text{ bytes in 1 MB}}
]
Simplification:
Using the properties of exponents, we can simplify this:
[
\frac{2^{40}}{2^{20}} = 2^{40 – 20} = 2^{20}
]
Thus, ( 2^{20} ) megabytes are in 1 terabyte.
Calculating ( 2^{20} ):
[
2^{20} = 1,048,576
]
Conclusion:
Therefore, 1 terabyte is equal to 1,048,576 megabytes (MB).
Explanation:
The binary system in computing uses powers of 2 to represent memory sizes because digital devices store and process data in binary form (using only 0s and 1s). A byte, which consists of 8 bits, is the fundamental unit of digital storage. Higher storage units like kilobytes (KB), megabytes (MB), gigabytes (GB), and terabytes (TB) are all based on powers of 2.
- 1 kilobyte (KB) = ( 2^{10} ) bytes = 1,024 bytes
- 1 megabyte (MB) = ( 2^{20} ) bytes = 1,048,576 bytes
- 1 gigabyte (GB) = ( 2^{30} ) bytes = 1,073,741,824 bytes
- 1 terabyte (TB) = ( 2^{40} ) bytes = 1,099,511,627,776 bytes
By dividing the number of bytes in a terabyte by the number of bytes in a megabyte, we arrive at the answer: 1 TB = 1,048,576 MB.