Units

All data in a computer is stored and processed using bits, which are the smallest unit of data and can hold just one of two values: 0 or 1. 

These binary digits are the foundation of all digital information, including text, images, video, and software. Because a single bit can only represent two states, we group them together to form larger, more useful units. Eight bits make one byte, which is enough to represent a single character like a letter or number.

As technology evolved and files grew larger, it became necessary to work with even bigger units. That's why we use kibibytes (KiB), mebibytes (MiB), gibibytes (GiB), and tebibytes (TiB)—each one is 1024 times larger than the previous.

We can convert between the different units by doing the following (step-up):

Examples

1. Convert 4096 bytes into kibibytes (KiB).
   Step-by-step:

• • Convert from bytes to KiB: 4096 ÷ 1024.

Expression:
4096 ÷ 1024

2. Convert 2.5 GiB into bits.
   Step-by-step:

• • Convert GiB to MiB: 2.5 × 1024
  • Convert MiB to KiB: × 1024
  • Convert KiB to bytes: × 1024
  • Convert bytes to bits: × 8

Expression:
2.5 × 1024 × 1024 × 1024 × 8

Edexcel GCSE Computer Science

When we measure file transfer speeds over a network, we often use bits rather than bytes. Common units include kilobits per second (Kb/s), megabits per second (Mb/s), and gigabits per second (Gb/s). 

These use the decimal system, so 1 kilobit = 1000 bits, 1 megabit = 1000 kilobits, and 1 gigabit = 1000 megabits. This is different from how we measure file sizes on storage devices (which use binary prefixes like kibibytes and mebibytes). 

To work out things like how long it will take to download a file or what size a file is based on speed and time, we often have to combine both sets of units in expressions. 

That might mean converting a file size in bytes into bits, or changing megabits per second into bits per second, so that all units match in the calculation.

We can convert between the different units by doing the following (step-up):

We can also do the opposite operations and set-down between the different units:

When working on GCSE questions surrounding file transfer you need to be aware of the following formula for working out total transfer time.

Transfer Time (seconds) = Bandwidth (bits per second) / File Size (bits)​

The formula may need to be rearranged, for example if you were asked to calculate the bandwidth based on transfer time and file size.

Examples

When working with GCSE exam questions you must remember that file size is represented in factors of 1024 and that bandwidth is represented in factors of 1000. Often you step down file size and bandwidth down to bits before dividing or multiplying to the requested unit.

1. Calculating transfer time: A file is 10 MiB in size. The network speed is 20 Mb/s. Write an expression to calculate how long it will take to transfer the file.

Steps:

• • Convert file size (10 MiB) to bytes: 10 × 1024 × 1024
  • Convert file size (bytes) bytes to bits: × 8
  • Convert 20 Mb/s to bits: 20 x 1000 x 1000
  • Divide both numbers (answer is represented in seconds)

Answer (Expression):
(10 × 1024 × 1024 × 8) ÷ (20 × 1000 x 1000)

2. Calculate Bandwidth: A 25 MiB file takes 10 seconds to transfer. Write an expression to calculate the bandwidth in Mb/s.

Steps:

• • Convert file size to bits: 25 × 1024 × 1024 × 8
  • Divide by time (10 seconds)
  • Convert bits per second to megabits per second: ÷ 1000 ÷ 1000

Answer (Expression):
(25 × 1024 × 1024 × 8) ÷ 10 ÷ 1000 ÷ 1000

3. Calculate File Size: A download takes 15 seconds at 50 Mb/s. Write an expression to calculate the file size in MiB.

Steps:

• • Convert bandwidth (50Mb/s) to bits: 50 × 1000 x 1000
  • Multiply bandwidth (bits/s) by seconds: x 15
  • Convert to bytes: ÷ 8
  • Convert to MiB: ÷ 1024 ÷ 1024

Answer (Expression):
(50 × 1000000 × 15) ÷ 8 ÷ 1024 ÷ 1024

 

Edexcel GCSE Computer Science