Representing bitmap images in binary

What you'll learn

What a bitmap image is and how it is built from pixels.
How resolution affects the amount of image data.
How colour depth controls the number of colours available.
How to estimate bitmap image data size using bits, bytes and KiB.

Starting point: binary data

Computers store all data using binary, which means using only the digits 0 and 1.

Definition

Bit

A bit is a single binary digit: either 0 or 1. It is the smallest unit of data a computer can store.

A picture cannot be stored as “a picture” directly. It must be broken down into values that can be represented in binary. For bitmap images, the key idea is: split the image into tiny squares, then store a binary value for each square.

Bitmap images and pixels

Definition

Bitmap image

A bitmap image is an image represented as a grid of tiny squares called pixels, where each pixel stores a colour value in binary.

Definition

Pixel

A pixel, short for “picture element”, is the smallest individual square of colour in a bitmap image.

If you zoom in far enough on a bitmap image, you can see the individual pixels. Each pixel has a colour, and that colour is stored using a binary code.

The computer also needs to know the order of the pixels. A simple way to imagine this is that it stores pixel values row by row, from left to right and top to bottom.

Bitmap image shown as an 8 by 6 pixel grid, with one pixel zoomed in to show a stored binary colour value

Black-and-white pixels

For a very simple black-and-white image, each pixel could be stored using just 1 bit:

0 could mean white
1 could mean black

The exact meaning of each value depends on the system or file format, but the principle is the same: each pixel’s colour is stored as binary.

Example

Encoding a tiny black-and-white image

Suppose 0 means white and 1 means black. A 3 pixel by 2 pixel image is stored row by row as:

0 1 0 1 1 0

Work out the resolution: the image is 3 pixels wide and 2 pixels high, so it has $\times 2 = 6$ pixels.
Split the data into rows of 3 pixels:
Row 1 is 0 1 0
Row 2 is 1 1 0
Convert each bit into a pixel colour:
Row 1 is white, black, white.
Row 2 is black, black, white.

Key Idea

Bitmap representation

A bitmap image is stored as binary colour values for each pixel in a grid.

Resolution

Definition

Resolution

Resolution is the number of pixels in an image, usually written as width in pixels by height in pixels.

For example, an image with a resolution of 800 by 600 has 800 pixels across each row and 600 rows of pixels.

To find the total number of pixels:

pixels=width×height\text{number of pixels} = \text{width} \times \text{height}

Higher resolution usually means the image can show more detail, because it has more pixels. However, it also means more pixel values must be stored.

Example

Finding the number of pixels

An image has a resolution of 1280 by 720. Find the total number of pixels.

Identify the width and height: width is 1280 pixels and height is 720 pixels.
Multiply width by height: $1280 \times 720 = 921\,600$ .
State the result with units: the image contains 921,600 pixels.

Common Mistake

Resolution is not the physical screen size

Resolution is measured in pixels, not centimetres or inches. A larger screen and a smaller screen could both display the same resolution.

Colour depth

Definition

Colour depth

Colour depth is the number of bits used to store the colour of each pixel. It is often measured in bits per pixel, sometimes shortened to bpp.

The more bits used per pixel, the more possible binary combinations there are. This means the image can use more possible colours.

The number of possible colours is:

depth\text{number of colours} = 2^{\text{colour depth}}

So:

1 bit per pixel gives 2 possible colours.
2 bits per pixel gives 4 possible colours.
3 bits per pixel gives 8 possible colours.
8 bits per pixel gives 256 possible colours.

Comparison of colour depth showing 1 bit per pixel gives 2 colours, 2 bits gives 4 colours, and 3 bits gives 8 colours

Why powers of 2?

Each bit has 2 possible states: 0 or 1. Adding another bit doubles the number of possible patterns.

For example, with 2 bits you can store:

00
01
10
11

That gives 4 possible values, so 4 possible colours.

Example

Working out possible colours

How many colours can be represented using a colour depth of 5 bits per pixel?

Use the colour depth formula: $depth\text{number of colours} = 2^{\text{colour depth}}$ .
Substitute the colour depth: $2^5 = 32$ .
Interpret the result: 5 bits per pixel can represent 32 possible colours.

Example

Choosing a suitable colour depth

A bitmap image needs at least 100 possible colours. What is the smallest colour depth that can be used?

Compare powers of 2 near 100: $2^6 = 64$ , which is too few colours.
Try the next colour depth: $2^7 = 128$ , which is enough colours.
Choose the smallest value that works: the image needs 7 bits per pixel.

Tip

Colour depth shortcut

Increasing colour depth by 1 bit doubles the number of possible colours.

Resolution and colour depth together

Resolution and colour depth affect different parts of the bitmap:

Resolution decides how many pixels there are.
Colour depth decides how many bits are stored for each pixel.

To estimate the image data size:

depth\begin{aligned} \text{number of pixels} &= \text{width} \times \text{height} \\ \text{image data size in bits} &= \text{number of pixels} \times \text{colour depth} \end{aligned}

This gives the size of the pixel data, not always the exact final file size.

Units for image size

You need to be comfortable with the storage units used in GCSE Computer Science:

1 nibble = 4 bits
1 byte = 8 bits
1 KiB = 1024 bytes
1 MiB = 1024 KiB

To convert bits into bytes, divide by 8.

To convert bytes into KiB, divide by 1024.

Example

Calculating bitmap image data size

A bitmap image is 640 pixels wide and 480 pixels high. It uses a colour depth of 8 bits per pixel. Calculate the image data size in KiB.

Find the total number of pixels: $640 \times 480 = 307\,200$ pixels.
Multiply by the colour depth to find the number of bits: $600307\,200 \times 8 = 2\,457\,600$ bits.
Convert bits into bytes: $2002\,457\,600 \div 8 = 307\,200$ bytes.
Convert bytes into KiB: $200÷1024=300307\,200 \div 1024 = 300$ KiB.

Common Mistake

Mixing up bits and bytes

Colour depth is usually given in bits per pixel, but file size is often asked for in bytes or KiB. Always convert bits to bytes by dividing by 8.

Image quality and file size trade-off

Increasing resolution usually improves detail because there are more pixels. Increasing colour depth usually improves colour accuracy because more colours are available.

However, both changes increase the amount of data stored.

Key Idea

The trade-off

Higher resolution and higher colour depth can improve image quality, but they also increase the image data size.

For example:

Doubling the width doubles the number of pixels.
Doubling the height doubles the number of pixels.
Increasing colour depth stores more bits for every pixel.

So a high-resolution image with a high colour depth can become very large.

Common Mistake

Real files may include extra data

Actual bitmap files can also store metadata, which is data about the image, such as width, height and colour depth. In GCSE calculations, unless the question gives extra metadata, calculate only the pixel data size.

How the computer reconstructs the image

When the image is loaded, the computer needs enough information to rebuild the grid:

The resolution tells it how wide and tall the pixel grid is.
The colour depth tells it how many bits to read for each pixel.
The binary colour values tell it what colour each pixel should be.

If any of this information is missing or interpreted incorrectly, the image may display wrongly.

Example

Interpreting stored pixel data

A simple image has a resolution of 4 by 2 and uses 1 bit per pixel. The pixel data is:

1 0 0 1 0 1 1 0

Use the resolution to find the row length: the image is 4 pixels wide, so each row contains 4 bits.
Split the data into rows:
Row 1 is 1 0 0 1
Row 2 is 0 1 1 0
Apply the colour rule: if 1 means black and 0 means white, the image has black pixels at the first and fourth positions of row 1, and the second and third positions of row 2.

Exam technique

In the exam

If you see resolution, multiply width by height to find the number of pixels.
If you see colour depth, multiply total pixels by bits per pixel to find the size in bits.
Check the requested unit carefully: divide by 8 for bytes, then by 1024 for KiB.

Self review

Check yourself

What is the difference between resolution and colour depth?
How many possible colours can be represented with 4 bits per pixel?
Why does increasing resolution increase the amount of data needed to store a bitmap image?

Representing bitmap images in binary

What you'll learn

What a bitmap image is and how it is built from pixels.
How resolution affects the amount of image data.
How colour depth controls the number of colours available.
How to estimate bitmap image data size using bits, bytes and KiB.

Starting point: binary data

Computers store all data using binary, which means using only the digits 0 and 1.

Definition

Bit

A bit is a single binary digit: either 0 or 1. It is the smallest unit of data a computer can store.

Bitmap images and pixels

Definition

Bitmap image

A bitmap image is an image represented as a grid of tiny squares called pixels, where each pixel stores a colour value in binary.

Definition

Pixel

A pixel, short for “picture element”, is the smallest individual square of colour in a bitmap image.

If you zoom in far enough on a bitmap image, you can see the individual pixels. Each pixel has a colour, and that colour is stored using a binary code.

The computer also needs to know the order of the pixels. A simple way to imagine this is that it stores pixel values row by row, from left to right and top to bottom.

Bitmap image shown as an 8 by 6 pixel grid, with one pixel zoomed in to show a stored binary colour value

Black-and-white pixels

For a very simple black-and-white image, each pixel could be stored using just 1 bit:

0 could mean white
1 could mean black

The exact meaning of each value depends on the system or file format, but the principle is the same: each pixel’s colour is stored as binary.

Example

Encoding a tiny black-and-white image

Suppose 0 means white and 1 means black. A 3 pixel by 2 pixel image is stored row by row as:

0 1 0 1 1 0

Work out the resolution: the image is 3 pixels wide and 2 pixels high, so it has $\times 2 = 6$ pixels.
Split the data into rows of 3 pixels:
Row 1 is 0 1 0
Row 2 is 1 1 0
Convert each bit into a pixel colour:
Row 1 is white, black, white.
Row 2 is black, black, white.

Key Idea

Bitmap representation

A bitmap image is stored as binary colour values for each pixel in a grid.

Resolution

Definition

Resolution

Resolution is the number of pixels in an image, usually written as width in pixels by height in pixels.

For example, an image with a resolution of 800 by 600 has 800 pixels across each row and 600 rows of pixels.

To find the total number of pixels:

pixels=width×height\text{number of pixels} = \text{width} \times \text{height}

Higher resolution usually means the image can show more detail, because it has more pixels. However, it also means more pixel values must be stored.

Example

Finding the number of pixels

An image has a resolution of 1280 by 720. Find the total number of pixels.

Identify the width and height: width is 1280 pixels and height is 720 pixels.
Multiply width by height: $1280 \times 720 = 921\,600$ .
State the result with units: the image contains 921,600 pixels.

Common Mistake

Resolution is not the physical screen size

Resolution is measured in pixels, not centimetres or inches. A larger screen and a smaller screen could both display the same resolution.

Colour depth

Definition

Colour depth

Colour depth is the number of bits used to store the colour of each pixel. It is often measured in bits per pixel, sometimes shortened to bpp.

The more bits used per pixel, the more possible binary combinations there are. This means the image can use more possible colours.

The number of possible colours is:

depth\text{number of colours} = 2^{\text{colour depth}}

So:

1 bit per pixel gives 2 possible colours.
2 bits per pixel gives 4 possible colours.
3 bits per pixel gives 8 possible colours.
8 bits per pixel gives 256 possible colours.

Comparison of colour depth showing 1 bit per pixel gives 2 colours, 2 bits gives 4 colours, and 3 bits gives 8 colours

Why powers of 2?

Each bit has 2 possible states: 0 or 1. Adding another bit doubles the number of possible patterns.

For example, with 2 bits you can store:

00
01
10
11

That gives 4 possible values, so 4 possible colours.

Example

Working out possible colours

How many colours can be represented using a colour depth of 5 bits per pixel?

Use the colour depth formula: $depth\text{number of colours} = 2^{\text{colour depth}}$ .
Substitute the colour depth: $2^5 = 32$ .
Interpret the result: 5 bits per pixel can represent 32 possible colours.

Example

Choosing a suitable colour depth

A bitmap image needs at least 100 possible colours. What is the smallest colour depth that can be used?

Compare powers of 2 near 100: $2^6 = 64$ , which is too few colours.
Try the next colour depth: $2^7 = 128$ , which is enough colours.
Choose the smallest value that works: the image needs 7 bits per pixel.

Tip

Colour depth shortcut

Increasing colour depth by 1 bit doubles the number of possible colours.

Resolution and colour depth together

Resolution and colour depth affect different parts of the bitmap:

Resolution decides how many pixels there are.
Colour depth decides how many bits are stored for each pixel.

To estimate the image data size:

depth\begin{aligned} \text{number of pixels} &= \text{width} \times \text{height} \\ \text{image data size in bits} &= \text{number of pixels} \times \text{colour depth} \end{aligned}

This gives the size of the pixel data, not always the exact final file size.

Units for image size

You need to be comfortable with the storage units used in GCSE Computer Science:

1 nibble = 4 bits
1 byte = 8 bits
1 KiB = 1024 bytes
1 MiB = 1024 KiB

To convert bits into bytes, divide by 8.

To convert bytes into KiB, divide by 1024.

Example

Calculating bitmap image data size

A bitmap image is 640 pixels wide and 480 pixels high. It uses a colour depth of 8 bits per pixel. Calculate the image data size in KiB.

Find the total number of pixels: $640 \times 480 = 307\,200$ pixels.
Multiply by the colour depth to find the number of bits: $600307\,200 \times 8 = 2\,457\,600$ bits.
Convert bits into bytes: $2002\,457\,600 \div 8 = 307\,200$ bytes.
Convert bytes into KiB: $200÷1024=300307\,200 \div 1024 = 300$ KiB.

Common Mistake

Mixing up bits and bytes

Colour depth is usually given in bits per pixel, but file size is often asked for in bytes or KiB. Always convert bits to bytes by dividing by 8.

Image quality and file size trade-off

Increasing resolution usually improves detail because there are more pixels. Increasing colour depth usually improves colour accuracy because more colours are available.

However, both changes increase the amount of data stored.

Key Idea

The trade-off

Higher resolution and higher colour depth can improve image quality, but they also increase the image data size.

For example:

Doubling the width doubles the number of pixels.
Doubling the height doubles the number of pixels.
Increasing colour depth stores more bits for every pixel.

So a high-resolution image with a high colour depth can become very large.

Common Mistake

Real files may include extra data

How the computer reconstructs the image

When the image is loaded, the computer needs enough information to rebuild the grid:

The resolution tells it how wide and tall the pixel grid is.
The colour depth tells it how many bits to read for each pixel.
The binary colour values tell it what colour each pixel should be.

If any of this information is missing or interpreted incorrectly, the image may display wrongly.

Example

Interpreting stored pixel data

A simple image has a resolution of 4 by 2 and uses 1 bit per pixel. The pixel data is:

1 0 0 1 0 1 1 0

Use the resolution to find the row length: the image is 4 pixels wide, so each row contains 4 bits.
Split the data into rows:
Row 1 is 1 0 0 1
Row 2 is 0 1 1 0
Apply the colour rule: if 1 means black and 0 means white, the image has black pixels at the first and fourth positions of row 1, and the second and third positions of row 2.

Exam technique

In the exam

If you see resolution, multiply width by height to find the number of pixels.
If you see colour depth, multiply total pixels by bits per pixel to find the size in bits.
Check the requested unit carefully: divide by 8 for bytes, then by 1024 for KiB.

Self review

Check yourself

What is the difference between resolution and colour depth?
How many possible colours can be represented with 4 bits per pixel?
Why does increasing resolution increase the amount of data needed to store a bitmap image?

Representing bitmap images in binary

What you'll learn

Starting point: binary data

Bitmap images and pixels

Black-and-white pixels

Resolution

Colour depth

Why powers of 2?

Resolution and colour depth together

Units for image size

Image quality and file size trade-off

How the computer reconstructs the image

You've reached the end

Representing bitmap images in binary

What you'll learn

Starting point: binary data

Bitmap images and pixels

Black-and-white pixels

Resolution

Colour depth

Why powers of 2?

Resolution and colour depth together

Units for image size

Image quality and file size trade-off

How the computer reconstructs the image

You've reached the end

Representing bitmap images in binary

What you'll learn

Starting point: binary data

Bitmap images and pixels

Black-and-white pixels

Resolution

Colour depth

Why powers of 2?

Resolution and colour depth together

Units for image size

Image quality and file size trade-off

How the computer reconstructs the image

You've reached the end

Representing bitmap images in binary Revision Guide

Representing bitmap images in binary

What you'll learn

Starting point: binary data

Bitmap images and pixels

Black-and-white pixels

Resolution

Colour depth

Why powers of 2?

Resolution and colour depth together

Units for image size

Image quality and file size trade-off

How the computer reconstructs the image

You've reached the end

Representing bitmap images in binary Revision Guide