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Data Representation - AQA Computer Science Cheat Sheet by [deleted]

Number Bases

Denary or Decimal
Base 10.
Base 2. Used by computers to represent all data and instru­ctions. Uses 1s and 0s to powers of 2 to represent whole numbers.
Base 16. Used in computing because more values can be repres­ented by fewer charac­ters. This makes it easier for humans to read and unders­tand.

Converting Between Number Bases

Denary to Binary
Divide by 2, then read the remainders backwards.
Binary to Denary
Multiply the binary numbers (i.e. every single digit) by the relevant place value, then add all of these together.
Denary to Hexade­cimal
Divide by 16, then read the divisors and remainder backwards. Then convert digits to hex digits.
Hexade­cimal to Denary
1. Separate the hex digits
2. Convert each digit to binary
3. Concat­enate, then convert to denary
Binary to Hexade­cimal
Convert to denary, then hex.
Hexade­cimal to Binary
Convert to denary, then binary.

Binary Addition

Binary Shifts

Binary shifts can be used for multip­lic­ation and division by powers of two.

Image: http:/­/wi­ki.s­ch­ool­cod­­m/g­cse­/da­ta-­rep­res­ent­ati­on/­num­ber­s/b­ina­ry-­shift/

Units of Inform­ation

A single binary digit.
8 bits.
1,000 bytes
1,000 kilobytes.
1,000 Megabytes.
1,000 Gigabytes.

ASCII vs Unicode

What is ASCII?
A character set that uses 7 bits, so can represent up to 128 charac­ters; this means that only Latin letters can be used (i.e. charac­ter­s/l­etters from other languages can't be repres­ented). However, it takes up less space that Unicode.
What is Unicode?
Unicode is also a character set, but it can represent many, many values, including non-La­tin­-based languages.

Repres­enting Images

A single point in a graphical issues. Short for 'picture element'.
A grid of pixels, with each pixel repres­ented by a binary number.
Colour depth
Number of colours that can (not necess­arily are) be repres­ented in an image, and the corres­ponding number of bits needed to represent each pixel (e.g. 2 bits for 4 colours). The greater the colour depth, the bigger the file size.
Resolution depth
How much detail there is in an image. The more pixels per inch, the higher the resolu­tion. The higher the resolu­tion, the bigger the file size.
Gives the software the inform­ation needed to display the image properly (size, resolution depth, colour depth).
Bitmap file size = width x height x colour depth (in bits)

Data Compre­ssion

Data compre­ssion is used to reduce file size, which means that they take up less storage space. Lossy compre­ssion is where some data is removed - this means that an image would lose some detail. Lossless compre­ssion preserves all of the inform­ation.

Run length encoding (RLE) uses data frequency pairs to reduce the amount of data stored. It does so by stating the character and then the length of the run. Example:
1001 1111 0101 can be shown as 1 1 2 0 5 1 1 0 1 1 1 0 1 1

Huffman coding is more efficient than RLE. It is also lossless. It finds the frequency of each data item to create a Huffman tree, which assigns the most frequent items the shortest code. When you move down a branch to the left, a 0 is assigned. When you move to the right, a 1 is assigned.
total bits needed = number of bits needed per character x number of characters

Repres­enting Sound

A measure of amplitude at a given point. Used to convert an analogue wave into a digital format.
Sampling rate
The number of samples taken in a second. Measured in Hertz.
Sampling resolution
The number of bits per sample.
Bit rate
The number of bits used per second of the audio. Usually measured in kilobits per second (kbps).
File size (bits) = sampling rate x resolution x lenght of recording (seconds)


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