CS12Representing Text, Images and Sound

Computers store everything in binary, so each letter, digit and symbol is given a number. A character set is the agreed list.

• Character set (AQA): “a collection of characters (letters, numbers, symbols, etc.) that a computer system can process and use to represent text, with each character assigned a unique numerical code.”
• Codes are grouped and run in sequence. In ASCII, 'A' is 65, 'B' is 66, 'C' is 67, and so on up to 'Z' at 90.
• The same is true for lower case ('a' is 97, 'b' is 98…) and for digits ('0' is 48, '1' is 49…).
• So if you know the code for the first character in a group, you can work out the rest: count on from it.
• Upper and lower case letters have different codes: 'a' (97) is 32 more than 'A' (65).
• The character '7' has the code 55. It is not the number 7.

Character set

A collection of characters (letters, numbers, symbols, etc.) that a computer system can process and use to represent text, with each character assigned a unique numerical code.

Character code

The number given to one character in a character set.

ASCII (AQA): “a character encoding system that uses a 7-bit notation that allows for the representation of 128 unique characters.”

• 7 bits give 2⁷ = 128 different codes: 0 to 127.
• ASCII covers the English alphabet in both cases, the digits 0–9, punctuation, the space (32) and some control codes.
• To convert a character to binary: find its decimal code (from a table or by counting on), then write it as a 7-bit binary number.
• To convert binary to a character: turn the 7-bit number into decimal, then look up or count to the character.
• Some books and videos mention 8-bit “extended ASCII”. AQA's ASCII is 7-bit.

ASCII

A character encoding system that uses a 7-bit notation that allows for the representation of 128 unique characters.

128 characters is enough for English, but not for the world's other alphabets, or for maths symbols and emoji. Unicode was introduced to fix that.

• Purpose: to represent the characters of many different alphabets (such as Greek, Arabic, Chinese and Hindi) and special symbols, “allowing a far greater range of characters.”
• AQA's vocabulary: Unicode was “introduced to support a wider range of characters due to increased communication across countries.” It can use up to 32 bits per character.
• Unicode now defines well over 100,000 characters. You don't need to learn a number.
• Unicode uses the same codes as ASCII up to 127, so 'A' is still 65. Text in ASCII is still valid in Unicode.
• Advantages over ASCII: many more characters, so text in any language, and emoji, can be stored and shared between countries and devices.
• Disadvantage: a character can need more bits than in ASCII, so text files can be larger.
• You don't need to know about UTF-8, UTF-16 or other versions of Unicode.

Unicode

A character set introduced to support a wider range of characters due to increased communication across countries; it can use up to 32 bits per character.

A bitmap image is a grid of dots. Each dot is a pixel, and each pixel's colour is stored as a binary code.

• Pixel: short for picture element. “A pixel is a single point in an image.”
• Bitmap (AQA): “images are broken down into a rectangular grid of pixels. Each pixel will have its own colour value.”
• The screen shows the image by lighting each pixel in its stored colour, row by row.
• Image size is given in pixels as width × height. A 640 × 480 image is 640 pixels wide and 480 pixels high.
• Number of pixels = width × height. 640 × 480 = 307,200 pixels.
• More pixels in the same space show more detail, but need more bits to store.

Pixel

Short for picture element. A single point in an image.

Bitmap

An image broken down into a rectangular grid of pixels, each with its own colour value.

Image size

The width × height of an image in pixels.

Colour depth is the number of bits used to represent each pixel. It sets how many colours the image can use.

• Each extra bit doubles the number of colours.
• Minimum colour depth for n colours: the smallest number of bits d where 2^d is at least n.
• 3 colours need 2 bits (2 bits give 4 codes; 1 bit gives only 2).
• 5 colours need 3 bits. 9 colours need 4 bits. 2 colours need just 1 bit.
• Adding a colour only makes the file bigger if it needs an extra bit: going from 5 to 8 colours still needs 3 bits; going from 8 to 9 needs 4.

Colour depth

The number of bits used to represent each pixel.

You may be given a bit pattern and asked to draw the image, or given an image and asked for its bit pattern. Work row by row, from the top left.

• Split the bit pattern into groups of colour depth bits. Each group is one pixel.
• Use the image width to split the pixels into rows: an 8-pixel-wide, 1-bit image has 8 bits per row.
• Use the key to turn each code into a colour, or each colour into a code.
• For an image to bit pattern: write the code for each pixel, left to right, then the next row.

With a colour depth of 1 bit, each pixel is one bit: here 0 is white and 1 is blue.

With a colour depth of 2 bits, each pixel takes two bits, and a key says which code is which colour.

For AQA, a bitmap's file size depends only on the number of pixels and the colour depth.

• Size in bits = W × H × D (width in pixels × height in pixels × colour depth in bits).
• Size in bytes = (W × H × D) ÷ 8.
• Then ÷ 1000 for kilobytes and ÷ 1000 again for megabytes (see the topic on number bases and units). AQA rejects 1024.
• Doubling the width doubles the file size. Doubling both the width and the height gives 4 times the pixels, so 4 times the size.
• Raising the colour depth from 4 to 8 bits doubles the size. Real image files also hold extra data (metadata), but AQA's calculations ignore it.

Sound is analogue: a continuous wave that can take any value. Computers can only store and process digital (binary) data, so sound must be converted.

• Analogue (AQA): “continuous data – can take any value in a given range.”
• A microphone turns sound into an analogue electrical signal. An analogue to digital converter (ADC) takes samples of it at regular intervals.
• A sample is a measure of amplitude at a point in time. Each sample is rounded to a whole number and stored in binary.
• Sampling rate: “the number of samples taken in a second”, measured in hertz (1 hertz = 1 sample per second). 44,100 Hz means 44,100 samples every second.
• Sample resolution: “the number of bits per sample”. 16 bits gives 2¹⁶ = 65,536 possible amplitude values; 8 bits gives 256.
• A higher sampling rate captures the wave's changes more closely; a higher resolution records each amplitude more precisely. Both make the digital sound closer to the original, and both make the file larger.

Sampling: the amplitude is measured at regular points in time and each measurement is stored as a binary number.

Analogue

Continuous data that can take any value in a given range.

Sample

A measure of amplitude at a point in time.

Sampling rate

The number of samples taken in a second, usually measured in hertz (1 hertz = 1 sample per second).

Sample resolution

The number of bits per sample.

Every second, the sound file stores (sampling rate) samples, each (resolution) bits long.

• File size (bits) = rate × res × secs: sampling rate (Hz) × sample resolution (bits) × length (seconds).
• ÷ 8 for bytes, then ÷ 1000 for kB and ÷ 1000 again for MB.
• Convert minutes to seconds first: 2 minutes = 120 seconds.
• Doubling the sampling rate, the resolution or the length doubles the file size.