Units

What you'll learn

What bits, bytes, kilobytes, megabytes and larger units mean.
Why computers store and process data using binary.
How to convert between storage units such as MB and GB.
How to calculate storage requirements for text, image and sound files.

Why computers use binary

A computer stores and processes data using binary, which means using only two possible values: 0 and 1.

Inside a computer, electronic circuits are easiest to build when they only need to recognise two states, such as on/off, high voltage/low voltage, or magnetised/not magnetised. These two states are represented as binary digits.

Definition

Bit

A bit is a single binary digit. It can store one value: either 0 or 1.

All data has to be converted into a binary format before a computer can process it. This includes:

text characters
images
sound
videos
instructions in programs

For example, a letter in a text file is stored as a binary pattern, an image is stored using binary values for pixels, and sound is stored using binary values for samples.

Key Idea

Everything becomes bits

Computers do not directly understand letters, pictures or sounds. They process patterns of bits, and software interprets those bit patterns as meaningful data.

Data storage units

A unit is a standard amount used for measuring something. In computing, data storage units measure how much data is stored or how much capacity a device has.

The smallest units are bits and bytes:

Unit	Meaning
bit	One binary digit: 0 or 1
nibble	4 bits
byte, B	8 bits

Larger storage units are built from bytes:

Unit	Meaning using OCR decimal prefixes
kilobyte, kB or KB	1,000 bytes
megabyte, MB	1,000 kB
gigabyte, GB	1,000 MB
terabyte, TB	1,000 GB
petabyte, PB	1,000 TB

The ladder below shows the storage units from smallest to largest, and the direction for multiplying or dividing when converting.

Data storage unit ladder from bit to petabyte

Common Mistake

Bits and bytes are not the same

A bit is one binary digit. A byte is 8 bits. If a file size formula gives an answer in bits, you must divide by 8 to convert it into bytes.

Common Mistake

1,000 or 1,024?

For OCR J277, use decimal prefixes unless told otherwise: 1 kB = 1,000 bytes, 1 MB = 1,000 kB, and so on. Using 1,024 is also accepted, especially if the question states it.

Converting between units

When moving from a larger unit to a smaller unit, multiply.

For example:

GB to MB: multiply by 1,000
MB to kB: multiply by 1,000
bytes to bits: multiply by 8

When moving from a smaller unit to a larger unit, divide.

For example:

MB to GB: divide by 1,000
kB to MB: divide by 1,000
bits to bytes: divide by 8

Example

Converting between MB and bytes

A file is 6 MB. Convert this to bytes.

Convert megabytes to kilobytes by multiplying by 1,000: $kB6\text{ MB} = 6{,}000\text{ kB}$ .
Convert kilobytes to bytes by multiplying by 1,000 again: $bytes6{,}000\text{ kB} = 6{,}000{,}000\text{ bytes}$ .
So 6 MB is 6,000,000 bytes.

Tip

Convert one step at a time

If you are unsure, write out the unit ladder first. Move one step at a time and multiply or divide at each step.

Capacity and file size

File size means how much storage a file needs.

Capacity means the maximum amount of data a storage device can hold. Storage devices have different fixed capacities, such as:

32 GB USB flash drive
256 GB solid-state drive
1 TB hard disk drive

A device cannot store more data than its capacity. If the total file sizes are larger than the device capacity, the files will not all fit.

Definition

Storage capacity

Storage capacity is the maximum amount of data that can be stored on a device or storage medium.

When calculating whether files will fit, convert everything into the same unit first.

Example

Checking whether files fit

A student has a 4 GB USB drive. They want to store:

1.5 GB of video files
900 MB of image files
700 MB of documents

Will the files fit?

Convert the USB drive capacity into MB: $MB4\text{ GB} = 4{,}000\text{ MB}$ .
Convert all file sizes into MB. The videos are $MB1.5\text{ GB} = 1{,}500\text{ MB}$ .
Add the file sizes: $3{,}100\text{ MB}$ .
Compare the total with the capacity: 3,100 MB is less than 4,000 MB, so the files will fit.

Calculating text file size

A text file stores characters, such as letters, numbers, spaces and punctuation marks. Each character is stored using a fixed number of bits, depending on the character set being used.

Definition

Character

A character is a single symbol in text, such as A, 7, ?, or a space.

Use this formula:

characters\text{text size (bits)} = \text{bits per character} \times \text{number of characters}

Then convert bits into bytes by dividing by 8.

Example

Calculating text file size

A text file contains 2,000 characters. Each character uses 8 bits. Calculate the file size in bytes.

Substitute into the text file formula: $size=8×2,000\text{text size} = 8 \times 2{,}000$ bits.
Calculate the size in bits: $\times 2{,}000 = 16{,}000\text{ bits}$ .
Convert bits to bytes by dividing by 8: $16,000 \div 8 = 2{,}000\text{ bytes}$ .

Calculating image file size

A digital image is made from pixels, which are tiny squares of colour. The number of pixels is found from the image width and height.

Definition

Colour depth

Colour depth is the number of bits used to store the colour of each pixel in an image.

Use this formula:

(px)\text{image size (bits)} = \text{colour depth} \times \text{height (px)} \times \text{width (px)}

Then divide by 8 to convert from bits to bytes.

Example

Calculating image file size

An image is 800 pixels wide and 600 pixels high. It has a colour depth of 24 bits. Calculate the file size in MB.

Substitute into the image formula: $size=24×600×800\text{image size} = 24 \times 600 \times 800$ bits.
Calculate the number of bits: $24 \times 600 \times 800 = 11{,}520{,}000\text{ bits}$ .
Convert bits to bytes: $11,520,000 \div 8 = 1{,}440{,}000\text{ bytes}$ .
Convert bytes to MB: $1,440,000 \div 1{,}000 \div 1{,}000 = 1.44\text{ MB}$ .

Calculating sound file size

A digital sound file is made by taking measurements of a sound wave many times per second.

Definition

Sample rate

Sample rate is the number of sound samples taken per second. It is usually measured in hertz, Hz.

Definition

Bit depth

Bit depth is the number of bits used to store each sound sample.

Use this formula:

depth\text{sound size (bits)} = \text{sample rate} \times \text{duration (s)} \times \text{bit depth}

Then divide by 8 to convert from bits to bytes.

Example

Calculating sound file size

A sound file has a sample rate of 8,000 Hz, lasts for 30 seconds, and uses a bit depth of 16 bits. Calculate the file size in kB.

Substitute into the sound formula: $size=8,000×30×16\text{sound size} = 8{,}000 \times 30 \times 16$ bits.
Calculate the number of bits: $8,000 \times 30 \times 16 = 3{,}840{,}000\text{ bits}$ .
Convert bits to bytes: $3,840,000 \div 8 = 480{,}000\text{ bytes}$ .
Convert bytes to kB: $480,000 \div 1{,}000 = 480\text{ kB}$ .

Metadata and real file sizes

The formulas above calculate the main data in the file. Real files may also contain metadata, which is extra data about the file.

For example, an image file might store metadata about:

image dimensions
date created
camera settings
file type

In GCSE calculations, you normally ignore metadata unless the question tells you to include it.

Key Idea

Use the formula the question needs

Text, image and sound files use different file-size formulas. Always choose the formula that matches the type of data.

Exam technique

In the exam

Convert all values into matching units before comparing capacities or adding file sizes.
If a formula gives an answer in bits, divide by 8 to get bytes before converting to kB, MB or GB.
Use 1,000 for kB, MB, GB, TB and PB conversions unless the question states 1,024.

Self review

Check yourself

Why must data be converted into binary before a computer can process it?
How many bits are in a nibble, and how many bits are in a byte?
Which formula would you use to calculate the size of an uncompressed sound file?

Units

What you'll learn

What bits, bytes, kilobytes, megabytes and larger units mean.
Why computers store and process data using binary.
How to convert between storage units such as MB and GB.
How to calculate storage requirements for text, image and sound files.

Why computers use binary

A computer stores and processes data using binary, which means using only two possible values: 0 and 1.

Definition

Bit

A bit is a single binary digit. It can store one value: either 0 or 1.

All data has to be converted into a binary format before a computer can process it. This includes:

text characters
images
sound
videos
instructions in programs

For example, a letter in a text file is stored as a binary pattern, an image is stored using binary values for pixels, and sound is stored using binary values for samples.

Key Idea

Everything becomes bits

Computers do not directly understand letters, pictures or sounds. They process patterns of bits, and software interprets those bit patterns as meaningful data.

Data storage units

A unit is a standard amount used for measuring something. In computing, data storage units measure how much data is stored or how much capacity a device has.

The smallest units are bits and bytes:

Unit	Meaning
bit	One binary digit: 0 or 1
nibble	4 bits
byte, B	8 bits

Larger storage units are built from bytes:

Unit	Meaning using OCR decimal prefixes
kilobyte, kB or KB	1,000 bytes
megabyte, MB	1,000 kB
gigabyte, GB	1,000 MB
terabyte, TB	1,000 GB
petabyte, PB	1,000 TB

The ladder below shows the storage units from smallest to largest, and the direction for multiplying or dividing when converting.

Data storage unit ladder from bit to petabyte

Common Mistake

Bits and bytes are not the same

A bit is one binary digit. A byte is 8 bits. If a file size formula gives an answer in bits, you must divide by 8 to convert it into bytes.

Common Mistake

1,000 or 1,024?

For OCR J277, use decimal prefixes unless told otherwise: 1 kB = 1,000 bytes, 1 MB = 1,000 kB, and so on. Using 1,024 is also accepted, especially if the question states it.

Converting between units

When moving from a larger unit to a smaller unit, multiply.

For example:

GB to MB: multiply by 1,000
MB to kB: multiply by 1,000
bytes to bits: multiply by 8

When moving from a smaller unit to a larger unit, divide.

For example:

MB to GB: divide by 1,000
kB to MB: divide by 1,000
bits to bytes: divide by 8

Example

Converting between MB and bytes

A file is 6 MB. Convert this to bytes.

Convert megabytes to kilobytes by multiplying by 1,000: $kB6\text{ MB} = 6{,}000\text{ kB}$ .
Convert kilobytes to bytes by multiplying by 1,000 again: $bytes6{,}000\text{ kB} = 6{,}000{,}000\text{ bytes}$ .
So 6 MB is 6,000,000 bytes.

Tip

Convert one step at a time

If you are unsure, write out the unit ladder first. Move one step at a time and multiply or divide at each step.

Capacity and file size

File size means how much storage a file needs.

Capacity means the maximum amount of data a storage device can hold. Storage devices have different fixed capacities, such as:

32 GB USB flash drive
256 GB solid-state drive
1 TB hard disk drive

A device cannot store more data than its capacity. If the total file sizes are larger than the device capacity, the files will not all fit.

Definition

Storage capacity

Storage capacity is the maximum amount of data that can be stored on a device or storage medium.

When calculating whether files will fit, convert everything into the same unit first.

Example

Checking whether files fit

A student has a 4 GB USB drive. They want to store:

1.5 GB of video files
900 MB of image files
700 MB of documents

Will the files fit?

Convert the USB drive capacity into MB: $MB4\text{ GB} = 4{,}000\text{ MB}$ .
Convert all file sizes into MB. The videos are $MB1.5\text{ GB} = 1{,}500\text{ MB}$ .
Add the file sizes: $3{,}100\text{ MB}$ .
Compare the total with the capacity: 3,100 MB is less than 4,000 MB, so the files will fit.

Calculating text file size

A text file stores characters, such as letters, numbers, spaces and punctuation marks. Each character is stored using a fixed number of bits, depending on the character set being used.

Definition

Character

A character is a single symbol in text, such as A, 7, ?, or a space.

Use this formula:

characters\text{text size (bits)} = \text{bits per character} \times \text{number of characters}

Then convert bits into bytes by dividing by 8.

Example

Calculating text file size

A text file contains 2,000 characters. Each character uses 8 bits. Calculate the file size in bytes.

Substitute into the text file formula: $size=8×2,000\text{text size} = 8 \times 2{,}000$ bits.
Calculate the size in bits: $\times 2{,}000 = 16{,}000\text{ bits}$ .
Convert bits to bytes by dividing by 8: $16,000 \div 8 = 2{,}000\text{ bytes}$ .

Calculating image file size

A digital image is made from pixels, which are tiny squares of colour. The number of pixels is found from the image width and height.

Definition

Colour depth

Colour depth is the number of bits used to store the colour of each pixel in an image.

Use this formula:

(px)\text{image size (bits)} = \text{colour depth} \times \text{height (px)} \times \text{width (px)}

Then divide by 8 to convert from bits to bytes.

Example

Calculating image file size

An image is 800 pixels wide and 600 pixels high. It has a colour depth of 24 bits. Calculate the file size in MB.

Substitute into the image formula: $size=24×600×800\text{image size} = 24 \times 600 \times 800$ bits.
Calculate the number of bits: $24 \times 600 \times 800 = 11{,}520{,}000\text{ bits}$ .
Convert bits to bytes: $11,520,000 \div 8 = 1{,}440{,}000\text{ bytes}$ .
Convert bytes to MB: $1,440,000 \div 1{,}000 \div 1{,}000 = 1.44\text{ MB}$ .

Calculating sound file size

A digital sound file is made by taking measurements of a sound wave many times per second.

Definition

Sample rate

Sample rate is the number of sound samples taken per second. It is usually measured in hertz, Hz.

Definition

Bit depth

Bit depth is the number of bits used to store each sound sample.

Use this formula:

depth\text{sound size (bits)} = \text{sample rate} \times \text{duration (s)} \times \text{bit depth}

Then divide by 8 to convert from bits to bytes.

Example

Calculating sound file size

A sound file has a sample rate of 8,000 Hz, lasts for 30 seconds, and uses a bit depth of 16 bits. Calculate the file size in kB.

Substitute into the sound formula: $size=8,000×30×16\text{sound size} = 8{,}000 \times 30 \times 16$ bits.
Calculate the number of bits: $8,000 \times 30 \times 16 = 3{,}840{,}000\text{ bits}$ .
Convert bits to bytes: $3,840,000 \div 8 = 480{,}000\text{ bytes}$ .
Convert bytes to kB: $480,000 \div 1{,}000 = 480\text{ kB}$ .

Metadata and real file sizes

The formulas above calculate the main data in the file. Real files may also contain metadata, which is extra data about the file.

For example, an image file might store metadata about:

image dimensions
date created
camera settings
file type

In GCSE calculations, you normally ignore metadata unless the question tells you to include it.

Key Idea

Use the formula the question needs

Text, image and sound files use different file-size formulas. Always choose the formula that matches the type of data.

Exam technique

In the exam

Convert all values into matching units before comparing capacities or adding file sizes.
If a formula gives an answer in bits, divide by 8 to get bytes before converting to kB, MB or GB.
Use 1,000 for kB, MB, GB, TB and PB conversions unless the question states 1,024.

Self review

Check yourself

Why must data be converted into binary before a computer can process it?
How many bits are in a nibble, and how many bits are in a byte?
Which formula would you use to calculate the size of an uncompressed sound file?

Units

What you'll learn

Why computers use binary

Data storage units

Converting between units

Capacity and file size

Calculating text file size

Calculating image file size

Calculating sound file size

Metadata and real file sizes

Recap questions

You've reached the end

Units

What you'll learn

Why computers use binary

Data storage units

Converting between units

Capacity and file size

Calculating text file size

Calculating image file size

Calculating sound file size

Metadata and real file sizes

Recap questions

You've reached the end

Units

What you'll learn

Why computers use binary

Data storage units

Converting between units

Capacity and file size

Calculating text file size

Calculating image file size

Calculating sound file size

Metadata and real file sizes

Recap questions

You've reached the end

Units Revision Guide

Units

What you'll learn

Why computers use binary

Data storage units

Converting between units

Capacity and file size

Calculating text file size

Calculating image file size

Calculating sound file size

Metadata and real file sizes

Recap questions

You've reached the end

Units Revision Guide