1 gigabyte in binary system is equivalent to

Correct — B, 1024 megabytes. In the binary system used for computer memory, each step up the scale is a factor of 2 to the power of 10, that is 1024, rather than a round 1000. So 1 kilobyte is 1024 bytes, 1 megabyte is 1024 kilobytes, 1 gigabyte is 1024 megabytes, and 1 terabyte is 1024 gigabytes. The question specifies the binary system explicitly, so the answer is 1024 megabytes; expressed in kilobytes the same quantity would be 1024 multiplied by 1024, which is 1,048,576.

• (a)1000 kilobytes — Wrong on both counts. It uses the decimal factor of 1000, and it is one step short in the scale — 1000 kilobytes is roughly a megabyte, not a gigabyte.
• (c)1200 megabytes — 1200 is neither the binary factor of 1024 nor the decimal factor of 1000, and no counting system in use gives it.
• (d)10000 kilobytes — Off by more than two orders of magnitude. A gigabyte is about 1,048,576 kilobytes in binary counting, not ten thousand.

Two counting conventions run side by side. Manufacturers of storage devices use decimal prefixes, where a gigabyte is 1,000,000,000 bytes, because that is what the international system of units means by giga. Computer memory is organised in powers of two, so operating systems have traditionally reported a gigabyte as 1,073,741,824 bytes, that is 1024 cubed. The gap explains why a drive sold as 500 gigabytes shows as roughly 465 on screen. The binary units were later given distinct names — kibibyte, mebibyte, gibibyte — but the older usage of kilobyte and megabyte for the binary quantities remains common, and this question follows it.

The stem removes the ambiguity by saying 'in binary system', so the multiplier must be 1024 and not 1000. After that the only thing to check is the step: the question moves from gigabyte to megabyte, which is one step, so a single factor of 1024 is needed and not two. Options (a) and (d) both quote kilobytes, which is two steps down, and neither figure is right for two steps either.

• In binary counting, 1 kilobyte = 1024 bytes, 1 megabyte = 1024 kilobytes and 1 gigabyte = 1024 megabytes.
• 1024 is 2 to the power of 10, which is why it is the natural step in a binary machine.
• One gigabyte equals 1,073,741,824 bytes in binary counting.
• Storage manufacturers use decimal prefixes, where a gigabyte is 1,000,000,000 bytes.
• The binary units have formal names of their own — kibibyte, mebibyte, gibibyte.

• Using 1000 when the question specifies the binary system.
• Skipping or adding a step in the ladder — kilobyte, megabyte, gigabyte, terabyte.
• Confusing megabytes with megabits when reading transfer speeds; eight bits make a byte.

A one-step unit conversion, with distractors that fail either on the multiplier or on the number of steps.

No directly related past PYQ was found.

• practice — not a real PYQ

  How many bytes are there in one kilobyte in the binary system?

  • (a)1000
  • (b)1024
  • (c)512
  • (d)2048

  Answer(b) 1024 — that is 2 to the power of 10, the natural step in a binary machine.

• practice — not a real PYQ

  One terabyte is equal to

  • (a)1024 megabytes
  • (b)1024 gigabytes
  • (c)1000 gigabytes
  • (d)1024 kilobytes

  Answer(b) 1024 gigabytes — each rung of the binary ladder multiplies by 1024.