Size Matters (Binary Edition)

How big is that file?

Everything a computer stores is made of bits - single binary digits, each a 0 or a 1. Group them up and you can measure the size of a photo, a song or a whole hard drive. This module climbs the units ladder from a single bit to a tebibyte, and shows why this exam board counts storage in steps of 1024, not 1000.

The smallest units

Start at the bottom of the ladder:

Climb the units ladder

Put these storage units in order, from the SMALLEST to the LARGEST.

• Bit
• Nibble
• Byte
• Kibibyte (KiB)
• Mebibyte (MiB)
• Gibibyte (GiB)
• Tebibyte (TiB)

The 1024 rule

This board uses IEC binary prefixes, so each step up the ladder multiplies by 1024, which is 2^10 - NOT 1000. 1 KiB = 1024 bytes, 1 MiB = 1024 KiB, 1 GiB = 1024 MiB, and 1 TiB = 1024 GiB. If you have also met the decimal prefixes (kB = 1000 bytes), you must switch conventions here, or every storage calculation will drift further out with each unit step. Always show the power-of-two working.

Bytes in a kibibyte

Using this board's binary prefixes, how many bytes are there in 1 kibibyte (KiB)?

Which statement is correct?

Under the binary (IEC) prefixes this board uses, which of these is TRUE?

• 1 MiB = 1024 KiB
• 1 MiB = 1000 KiB
• 1 MiB = 1024 bytes
• 1 KiB = 1024 bits

Convert the file size

A file is 3 MiB. Using 1 MiB = 1024 KiB, work out its size in kibibytes. The working is 3 x 1024. How many KiB is that?

Two prefix systems

The same letters can mean different amounts. Knowing which system you are in matters.

Match each unit to its size

Storage in words

A single binary digit is a _____. Eight of them make a _____. This board measures storage with _____ prefixes, so 1 kibibyte is _____ bytes. Because a value is stored in a fixed number of bits, there is a limit to the _____ whole number it can hold.

Limits of binary

A value is always stored in a fixed number of bits. Select the TWO true statements about this limit.

• A fixed number of bits limits the largest whole number you can store
• Storing fractions in a fixed number of bits can lose precision
• Adding more bits always makes stored numbers less accurate
• Eight bits can represent any whole number exactly

Binary units

Tap the TWO statements that are TRUE.

• One kibibyte is 1024 bytes, not 1000 bytes.
• Each step up the binary units ladder multiplies by 1024.
• One mebibyte is 1000 kibibytes under IEC binary prefixes.
• A nibble is larger than a byte.
• A bit and a byte are the same size.

The storage showdown

Work through three storage decisions, using this board's binary prefixes.

• A file is 2048 KiB. How many MiB is that?
• A drive has 4 GiB free. Each video is 512 MiB. How many videos fit?
• You must store a backup that has to be restored perfectly, byte for byte. Which compression should you choose?

Why 1024, not 1000?

Explain how this board measures data storage. Cover the units from bit to gibibyte, the size of each step, and why using the wrong convention would make a large storage calculation go wrong.

• Name the units in order and give the size of a bit, a nibble and a byte
• State the binary prefixes and that each step multiplies by 1024
• Give a short worked example, for example converting MiB to KiB
• Explain why using 1000 instead of 1024 would make a large calculation increasingly wrong