CPX6Representing Text, Images and Sound

ASCII is a standard for encoding characters (letters, digits, punctuation and control codes). It gives every character its own unique number, stored in binary.

• ASCII uses 7 bits per character, so it has 2⁷ = 128 codes (0 to 127).
• Codes 0–31 are control codes, such as carriage return and tab: they control devices rather than print a symbol.
• Codes are grouped and in sequence: capital letters run A–Z from 65, small letters a–z from 97, and digits 0–9 from 48.
• So if you know one code you can work out another: D is 3 after A, so D = 65 + 3 = 68.
• A small letter's code is 32 more than its capital (a = 97, A = 65).
• The digit character '7' (code 55) is not the number 7: it is a symbol with its own code.

Character set

The set of characters a computer can represent, each with a unique binary code.

ASCII

A 7-bit character encoding standard with 128 codes (0 to 127); codes 0–31 are control codes.

Control code

A non-printing character that controls a device, such as a new line.

• 128 codes are enough for English letters, digits and punctuation, but not for accented letters, other alphabets (Greek, Arabic, Chinese) or emoji.
• Other character sets use more bits per character, so they can represent many more characters, including non-English ones.
• You only need to know that these alternatives exist (extended ASCII and Unicode are examples). You don't need their details.

A bitmap image is a grid of pixels (picture elements). A pixel is the smallest element of a bitmap, and each pixel's colour is stored as a binary code.

• The size of an image is its width × height in pixels: the boat is 6 × 5 pixels (30 pixels).
• More pixels means more detail, but more bits to store.
• File size in bits = width × height × colour depth, plus metadata. Building these into expressions in KiB or MiB is in the storage units and file sizes topic.

Each pixel's colour is a 2-bit code

Pixel

Picture element: the smallest element of a bitmap image.

Bitmap

An image stored as a grid of pixels, each with a binary colour code.

Image size

The width × height of an image in pixels.

Colour depth is the number of bits used to represent the colour of each pixel.

• n bits per pixel give 2ⁿ colours: the more bits, the more colours or shades can be shown.
• Each extra bit doubles the number of colours.
• A greater colour depth means more bits per pixel, so a larger file. Doubling the colour depth doubles the pixel data.
• To find the minimum colour depth for a number of colours, find the smallest n where 2ⁿ is at least that number: 12 colours need 4 bits (2³ = 8 is too few).

Colour depth

The number of bits used to represent the colour of each pixel.

For Pearson, resolution is the number of pixels per inch (ppi). It sets how big the image is when it is displayed or printed.

• Printed width in inches = width in pixels ÷ ppi. A 200 × 100 pixel image at 100 ppi is 2 in × 1 in; at 200 ppi it is 1 in × 0.5 in.
• Higher resolution = more pixels per inch, so each pixel is smaller and the image looks sharper.
• A low-resolution image stretched to fill a bigger space has fewer pixels per inch, so each pixel shows up as a visible block: the image is pixelated.

Same pixels, different pixels per inch

Resolution

The number of pixels per inch (ppi), which sets the physical size of an image when it is displayed or printed.

Pixelation

When individual pixels can be seen as blocks, because there are too few pixels per inch.

Metadata is data about the file: information about the properties of the image, stored in the file alongside the pixel data.

• Examples: width and height in pixels, colour depth, resolution, date and time taken, camera model, location.
• The computer needs some of it (width, height, colour depth) to rebuild the image from the bits.
• Metadata adds to the file size, on top of the pixel data.

Metadata

Data about a file, such as an image's width, height, colour depth and the date it was taken; it adds to the file size.

• Pearson reads the bits from the top-left pixel, left to right along each row, then row by row down to the bottom-right pixel.
• Binary to image: split the bits into groups of the colour depth (1 bit, 2 bits…), then colour one pixel per group using the key.
• Image to binary: write each pixel's code in the same order.
• Number of bits for the pixels = width × height × colour depth.

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Sound is an analogue signal: it varies continuously. A computer stores it as digital data: a series of discrete values. Turning one into the other is called sampling.

• CD quality: a sample rate of 44.1 kHz (44 100 samples a second), a bit depth of 16, and stereo (2 channels).
• Higher sample rate (shorter sample interval): more samples a second, so the changes in the wave are captured more closely.
• Greater bit depth: more possible values for each sample, so each amplitude is stored more precisely.
• Both make the recording more accurate but the file larger. File size in bits = sample rate × bit depth × duration in seconds × channels (expressions are in the storage units topic).
• A digital recording is never a perfect copy: it only has the amplitude at the sample points, and each value is rounded to the nearest level the bit depth allows.

Samples taken at equal intervals, each stored with 3 bits

Analogue

Continuously varying.

Digital

Made of discrete (separate) values.

Sample rate

The number of samples taken per second, measured in hertz.

Sample interval

The time between samples.

Bit depth

The number of bits used to represent each sound sample.

The number of bits available sets how many different values can be represented: n bits give 2ⁿ. More bits give a wider range, but take more storage.