Information representation

Paper 1 · Unit 1. Number representations, multimedia and compression: calculations here are reliable marks.

1. Binary and decimal prefixes

Decimal prefixes go up in powers of 10; binary prefixes go up in powers of 2. Storage is often sold in decimal units, but computers measure in binary units, which is why a “1 TB” drive shows less than 1 TiB.

Decimal prefix	Value	Binary prefix	Value
kilo (kB)	10³ = 1000 bytes	kibi (KiB)	2¹⁰ = 1024 bytes
mega (MB)	10⁶ bytes	mebi (MiB)	2²⁰ = 1 048 576 bytes
giga (GB)	10⁹ bytes	gibi (GiB)	2³⁰ = 1 073 741 824 bytes
tera (TB)	10¹² bytes	tebi (TiB)	2⁴⁰ bytes

2. Number systems and representations

Representation	How it works	Example (8 bits)
Unsigned binary	Base 2; positive whole numbers only, 0 to 255	46 = 0010 1110
Hexadecimal	Base 16; one hex digit = 4 bits	46 = 2E
One’s complement	Negative = invert every bit of the positive value; range −127 to +127, with two zeros	−46 = 1101 0001
Two’s complement	Most significant bit is negative (−128); negative = invert and add 1; range −128 to +127	−46 = 1101 0010
BCD	Each denary digit stored separately in 4 bits	46 = 0100 0110

3. Binary addition, subtraction and overflow

Add binary numbers column by column, carrying 1 when a column totals 2 or 3. To subtract, add the two’s complement of the number being subtracted: 20 − 7 = 20 + (−7) = 0001 0100 + 1111 1001 = 0000 1101 (13), ignoring the final carry out.

Overflow happens when a result is too large (or too negative) to be stored in the available bits. In two’s complement it shows when adding two positives gives a negative result, or two negatives give a positive result: for example 100 + 50 = 150, which is outside −128 to +127.

4. Uses of BCD and hexadecimal

• BCD: digital displays such as clocks and calculators, where each digit is shown separately; financial and banking systems, where denary values such as currency must be stored exactly without rounding errors.
• Hexadecimal: memory addresses and dumps, HTML/CSS colour codes, MAC addresses, error codes. It is shorter than binary and easier for people to read and check.

5. Character sets

Character set	Bits per character	Characters	Notes
ASCII	7	128	English letters, digits, punctuation and control codes
Extended ASCII	8	256	Adds accented letters and symbols
Unicode	Up to 32 (variable, e.g. UTF-8)	Over a million	Every writing system and emojis; the first 128 codes match ASCII

Character codes are consecutive, so ‘B’ is one more than ‘A’. You do not need to memorise any codes.

6. Bitmap images

A bitmap is a grid of pixels; each pixel’s colour is stored as a binary value. The file header stores data about the image, such as its width, height, colour depth and file type.

Term	Meaning
Image resolution	The number of pixels in the image (width × height)
Screen resolution	The number of pixels a screen can display
Colour depth / bit depth	The number of bits per pixel: n bits give 2ⁿ colours

File size (bits) ≈ width × height × colour depth, plus the header. Increasing resolution or colour depth improves quality but increases file size.

7. Vector graphics

A vector graphic stores an image as a drawing list: a set of commands that define drawing objects (lines, circles, rectangles, text). Each object has properties, such as position, size, line colour, fill colour and line thickness.

Use a bitmap when…	Use a vector when…
The image is a photograph or has complex colour changes	The image is made of shapes, e.g. a logo, diagram or icon
Every pixel needs to be edited	It must be resized without losing quality
	A small file is needed for a simple image

8. Sound

Sound is an analogue wave. To store it, an analogue-to-digital converter samples the amplitude at regular intervals.

• Sampling rate: the number of samples per second (Hz). Higher = more accurate, larger file.
• Sampling resolution: the number of bits per sample. Higher = more accurate amplitude, larger file.

File size (bits) = sampling rate × sampling resolution × length (s) × channels.

9. Compression

	Lossy	Lossless
How	Permanently removes data that is less noticeable	Reduces size without losing any data; the original is rebuilt exactly
Examples	JPEG photos, MP3 audio, streamed video	RLE, PNG, ZIP, FLAC audio
Use when	Small files matter more than perfect quality, e.g. streaming	Every bit must be kept, e.g. text, program files, medical images

How each type of file can be compressed

• Text: lossless only, e.g. RLE for repeated characters, or replacing repeated words with shorter codes (dictionary coding).
• Bitmap: RLE stores runs of the same colour as a count and a colour; lossy methods reduce resolution or colour depth, or remove detail the eye won’t notice.
• Vector: simplify the drawing list, e.g. fewer objects or fewer points, and remove redundant properties.
• Sound: lossy perceptual coding removes sounds humans cannot hear or that are masked by louder sounds; or reduce sampling rate or resolution. Lossless formats such as FLAC keep all data.

RLE example: the pixel row WWWWWWBBBWW can be stored as 6W 3B 2W.

10. Examiner tips

1. Kibi vs kilo: use 1024 for KiB, MiB…, and 1000 for kB, MB…. Read which one the question uses.
2. Show your working in conversions and file-size calculations; method marks are available.
3. Two’s complement subtraction: add the negative; ignore the final carry out of the 8th bit.
4. Explain overflow in terms of the result needing more bits than are available.
5. BCD is not binary: 46 in BCD is 0100 0110, not 0010 1110.
6. Vector answers: use the words drawing list, drawing object and property.
7. Justify the compression method for the situation, e.g. lossless for a text file because no data may be lost.
8. Remember the file header when asked what a bitmap file contains.

11. Practice questions

12. Topic test: predict your grade