$2^{30}$ bytes and $2^{50}$ bytes are respectively equal to ........ and ........ .

Question

Accepted Answer

The correct option is (2):
In computer science, memory and storage capacity are typically measured using units based on powers of two, where a unit prefix represents $2^{10}$ (1024) of the preceding unit. To determine the correct answer, you must recall the standard hierarchy of binary prefixes. We know that $2^{10}$ bytes is 1 Kilobyte (KB), $2^{20}$ bytes is 1 Megabyte (MB), and $2^{30}$ bytes is 1 Gigabyte (GB). Following this pattern, an additional $2^{10}$ factor is added for each subsequent unit: $2^{40}$ bytes is 1 Terabyte (TB), and $2^{50}$ bytes is 1 Petabyte (PB). Therefore, $2^{30}$ bytes equals 1 Gigabyte, and $2^{50}$ bytes equals 1 Petabyte, making the pair in Option 2 the correct match. Mastering these powers of two is essential for understanding data capacity.

The incorrect option is (1):
Option 1 suggests "1 Megabyte, 1 Terabyte," which is incorrect because it misidentifies both terms. A Megabyte (MB) is defined as $2^{20}$ bytes, not $2^{30}$ bytes, which represents a factor of 1,024 times smaller than a Gigabyte. The second unit, Terabyte (TB), is defined as $2^{40}$ bytes, which is $2^{10}$ (or 1024) times smaller than the required $2^{50}$ bytes. This option mistakenly positions the values two steps lower than the required Gigabyte and one step lower than the required Petabyte in the storage hierarchy.

The incorrect option is (3):
Option 3, "1 Exabyte, 1 Zettabyte," is incorrect as it refers to units significantly larger than the given values. An Exabyte (EB) is equivalent to $2^{60}$ bytes, meaning this unit is $2^{30}$ (approximately a billion) times larger than the required $2^{30}$ bytes. Similarly, a Zettabyte (ZB) is $2^{70}$ bytes, making it $2^{20}$ times larger than the required $2^{50}$ bytes. These units belong to the far upper end of the data storage spectrum, often used for discussing extremely large cloud or scientific data centers.

The incorrect option is (4):
Option 4 suggests "1 Terabyte, 1 Yottabyte," which is incorrect due to a mismatch in the power of two values. Terabyte (TB) is $2^{40}$ bytes, while the question asks for $2^{30}$ bytes, creating an inaccuracy in the first term. Furthermore, a Yottabyte (YB) is an enormous unit, representing $2^{80}$ bytes. The Yottabyte is $2^{30}$ times larger than the required $2^{50}$ bytes. This pairing confuses two distant tiers in the binary storage hierarchy.