3.3 Fundamentals of data representation

• Number bases include decimal (base 10), binary (base 2), and hexadecimal (base 16).
• Computers use binary to represent all data and instructions.
• A bit pattern could represent different types of data including text, image, sound and integer.
• Hexadecimal is often used in computer science due to its ability to represent large numbers.
• Binary can be used to represent whole numbers.
• Students must be able to represent decimal values between 0 and 255 in binary.
• Hexadecimal can be used to represent whole numbers.
• Students must be able to represent decimal values between 0 and 255 in hexadecimal.
• Students must be able to convert in both directions between binary and decimal, binary and hexadecimal, and decimal and hexadecimal.
• A bit is the fundamental unit of information.
• A byte is a group of 8 bits.
• A bit is either a 0 or a 1.
• b represents bit.
• B represents byte.
• Quantities of bytes can be described using prefixes.
• The International System of Units (SI units) kilo, mega and so forth refer to values based on powers of 10.
• When referring to powers of 2 the terms kibi, mebi and so forth would normally be used but students do not need to know these.
• Students will need to be able to add together up to three binary numbers.
• Students will need to be able to apply a binary shift to a binary number.
• Students should be able to use a given character encoding table to: convert characters to character codes and convert character codes to characters.
• Character codes are commonly grouped and run in sequence within encoding tables.
• Students should know that character codes are grouped and that they run in sequence.
• Unicode uses the same codes as ASCII up to 127.
• Unicode allows a far greater range of characters due to its ability to represent large numbers.
• A pixel is a single point in an image.
• The size of a bitmap image is measured in pixels (width x height).
• File size (bits) = rate x res x secs.
• Sampling rate is the number of samples taken in a second and is usually measured in hertz (1 hertz = 1 sample per second).
• Huffman trees are used to represent the Huffman code.
• Bitmaps are made from pixels.
• The number of pixels and colour depth can affect the file size of a bitmap image.
• secs = number of seconds
• The digital representation of sound in terms of sampling rate and sample resolution is:
• Data can be compressed using run length encoding (RLE).
• Data compression is the process of reducing the amount of data required to represent a piece of data.
• H = image height.
• A sample is a measure of amplitude at a point in time.
• File size (bits) = (bits) = W x H x D.
• Sound file sizes can be calculated based on the sampling rate and the sample resolution:
• res = sample resolution