Arrange the following units of measure for digital information into correct order, starting with the smallest unit first and going to the largest unit : a. Kilobyte b. Byte c. Megabyte d. Terabyte e. Gigabyte f. Bit

Correct — option (2), f b a c e d.

Step 1, the two smallest units. A bit (item f) is one binary digit, 0 or 1. A byte (item b) is 8 bits: the US National Institute of Standards and Technology (NIST) gives one byte as 2³ = 8 bits. So bit comes first, then byte.

Step 2, the prefixes. Kilo, mega, giga and tera stand for 10³, 10⁶, 10⁹ and 10¹², so each step up multiplies by 1,000 in the decimal convention.

Step 3, reading the letters in order: Bit (item f), Byte (item b), Kilobyte (item a), Megabyte (item c), Gigabyte (item e), Terabyte (item d) gives f b a c e d.

The idea to remember: bit, byte, kilobyte, megabyte, gigabyte, terabyte; each prefix step is 1,000 times (decimal) or 1,024 times (binary).

Why the others are wrong

• (1)
  b f a d c e — This starts with byte before bit, but a byte is 8 bits, so the bit must come first.

  It also puts terabyte (item d) before megabyte (item c) and gigabyte (item e). Tera stands for 10¹², larger than mega (10⁶) and giga (10⁹), so the terabyte belongs at the end.

• (3)
  f b a d e c — The first three are right: bit, byte, kilobyte. The last three are reversed, reading terabyte, gigabyte, megabyte, which runs from largest to smallest.

  In ascending order a megabyte (10⁶ bytes) comes before a gigabyte (10⁹ bytes) and then a terabyte (10¹² bytes).

• (4)
  b f a c d e — It makes two swaps. Byte is placed before bit, though a byte is made of 8 bits.

  Terabyte (item d) is placed before gigabyte (item e), though a gigabyte is 10⁹ bytes and a terabyte 10¹² bytes. Only the middle, kilobyte then megabyte, is in the right place.

Digital information is stored as bits, each 0 or 1. Eight bits make a byte, and larger units add a prefix to the byte.

Those prefixes are read in more than one way. In SI (decimal) terms a megabyte is 10⁶ bytes and a gigabyte 10⁹ bytes. In December 1998 the International Electrotechnical Commission (IEC) approved separate binary prefixes: kibi (2¹⁰ = 1,024), mebi (2²⁰), gibi (2³⁰) and tebi (2⁴⁰).

So 1 MiB is 1,048,576 bytes while 1 MB is 1,000,000 bytes. NIST notes the binary prefixes are not part of the SI.

Key facts

• One byte = 8 bits (NIST: 1 B = 2³ bit).
• Decimal prefixes: kilo = 10³, mega = 10⁶, giga = 10⁹, tera = 10¹².
• IEC binary prefixes, approved in December 1998: kibi 2¹⁰, mebi 2²⁰, gibi 2³⁰, tebi 2⁴⁰.
• 1 MiB = 1,048,576 bytes; 1 MB = 1,000,000 bytes; 1 GiB = 1,073,741,824 bytes; 1 GB = 1,000,000,000 bytes.
• Ascending order: bit, byte, kilobyte, megabyte, gigabyte, terabyte.

Common traps

• Swapping bit and byte: the bit is the smaller unit, and eight bits make one byte.
• Misplacing tera: kilo, mega, giga, tera rise in that order, so the terabyte is the largest of these units.
• Worrying about 1,000 versus 1,024: the size of each unit depends on the convention, but the order of the units is the same under the decimal and the binary convention.

UnlockIAS will link similar questions from RAS Pre 2013 here once that paper is published on this site.

• practice — not a real PYQ

  Using the IEC binary prefixes, one mebibyte (MiB) is equal to

  • (a)1,000,000 bytes
  • (b)1,048,576 bytes
  • (c)1,024 bytes
  • (d)1,073,741,824 bytes
  Answer(2) — 1 MiB = 2²⁰ bytes = 1,048,576 bytes. Option (1) is the decimal megabyte, option (3) is one kibibyte and option (4) is one gibibyte.
• practice — not a real PYQ

  Which one of the following is the largest quantity of data?

  • (a)10 gigabytes
  • (b)1 terabyte
  • (c)500 megabytes
  • (d)8,000 bits
  Answer(2) — 1 terabyte is 10¹² bytes. Option (1) is 10¹⁰ bytes, option (3) is 5 × 10⁸ bytes and option (4) is 1,000 bytes. The order holds under the binary convention too, since 1 tebibyte (2⁴⁰ bytes) exceeds 10 gibibytes.