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→Week 1
==== Classes ====
* Tuesday: synchronous (live) classes on Big Blue Button at 11:40 am - see login to learn.senecacollege.ca ("Blackboard") for details, go to SPO600, and select the "Tuesday Classes" option on the left-hand menu.
* Friday: these classes will usually be asynchronous (pre-recorded) - see this page for details each week.
==== How open source communities work ====
* Do the [[SPO600 Code Review Lab|Code Review Lab (Lab 1)]] as homework.
=== Week 1 - Class II ===
==== Binary Representation of Data ====
* Binary
** Binary is a system which uses "bits" (''binary digits'') to represent values.
** Each bit has one of two values, signified by the symbols 0 and 1. These correspond to:
*** Electrically: typically off/on, or low/high voltage, or low/high current. Many other electrical representations are possible.
*** Logically: false or true.
** Binary numbers are resistant to errors, especially when compared to other systems such as analog voltages.
*** To represent the numbers 0-5 as an analog electical value, we could use a voltage from 0 - 5 volts. However, if we use a long cable, there will be signal loss the voltage will drop: we could apply 5 volts on one end of the cable, but only observe (say) 4.1 volts on the other end of the cable. Alternately, electromagnetic interference from nearby devices could slight increase the signal.
*** If we use instead use the same voltages and cable length to carry a binary signal, where 0 volts = off and 5 volts = on, a signal that had degraded from 5 volts to 4.1 volts would still be counted as a "1" and a 0 volt signal with some stray electromagnetic interference presenting as (say) 0.4 volts would still be counted as "0". However, we will need to use multiple bits to carry larger numbers -- either in parallel (multiple wires side-by-side), or sequentially (multiple bits presented over the same wire in sequence).
* Integers
** Integers are the basic building block of binary numbering schemes.
** In an unsigned integer, the bits are numbered from right to left starting at 0, and the value of each bit is <code>2<sup>bit</sup></code>. The value represented is the sum of each bit multiplied by its corresponding bit value. The range of an unsigned integer is <code>0:2<sup>bits</sup>-1</code> where bits is the number of bits in the unsigned integer.
** Signed integers are generally stored in twos-complement format, where the highest bit is used as a sign bit. If that bit is set, the value represented is <code>-(!value)-1</code> where ! is the NOT operation (each bit gets flipped from 0→1 and 1→0)
* Fixed-point
** A fixed-point value is encoded the same as an integer, except that some of the bits are fractional -- they're considered to be to the right of the "binary point" (binary version of "decimal point" - or more generically, the ''radix point''). For example, binary 000001.00 is decimal 1.0, and 000001.11 is decimal 1.75.
** An alternative to fixed-point values is integer values in a smaller unit of measurement. For example, some accounting software may use integer values representing cents. For input and display purposes, dollar and cent values are converted to/from cent values.
* Floating-point
** Floating point numbers have three parts: a ''sign bit'' (0 for positive, 1 for negative), a ''mantissa'' or ''significand'', and an ''exponent''. The value is interpreted as <code>''sign'' mantissa * 2<sup>exponent</sup></code>.
** The most commonly-used floating point formats are defined in the [[IEEE 754]] standard.
* Sound
** Sound waves are air pressure vibrations
** Digital sound is most often represented in raw form as a series of time-based measurements of air pressure, called Pulse Coded Modulation (PCM)
** PCM takes a lot of storage, so sound is often compressed in either a lossless (perfectly recoverable) or lossy format (higher compression, but the decompressed data doesn't perfectly match the original data). To permit high compression ratios with minimal impact on quality, psychoacoustic compression is used - sound variations that most people can't perceive are removed.
* Graphics
** The human eye perceives luminance (brightness) as well as hue (colour). Our hue receptors are generally sensitive to three wavelengths: red, green, and blue (RGB). We can stimulate the eye to perceive most colours by presenting a combination of light at these three wavelengths.
** Digital displays emit RGB colours, which are mixed together and perceived by the viewer. For printing, cyan/yellow/magenta inks are used, plus black to reduce the amount of colour ink required to represent dark tones; this is known as CYMK colour.
** Images are broken into picture elements (''pixels'') and each pixel is usually represented by a group of values for RGB or CYMK channels, where each channel is represented by an integer or floating-point value. For example, using an 8-bit-per-pixel integer scheme (also known as 24-bit colour), the brightest blue could be represented as R=0,G=0,B=255; the brightest yellow would be R=255,G=255,B=0; black would be R=0,G=0,B=0; and white would be R=255,G=255,B=255. With this scheme, the number of unique colours available is 256^3 ~= 16 million.
** As with sound, the raw storage of sampled data requires a lot of storage space, so various lossy and lossless compression schemes are used. Highest compression is achieved with psychovisual compression (e.g., JPEG).
** Moving pictures (video, animations) are stored as sequential images, often compressed by encoding only the differences between frames to save storage space.
* Compression techniques
** Huffman encoding / Adaptive arithmetic encoding
*** Instead of fixed-length numbers, variable-length numbers are used, with the most common values encoded in the smallest number of bits. This is an effective strategy if the distribution of values in the data set is uneven.
** Repeated sequence encoding (1D, 2D, 3D)
*** Run length encoding is an encoding scheme that records the number of repeated values. For example, fax messages are encoded as a series of numbers representing the number of white pixels, then the number of black pixels, then white pixels, then black pixels, alternating to the end of each line. These numbers are then represented with adaptive artithmetic encoding.
*** Text data can be compressed by building a dictionary of common sequences, which may represent words or complete phrases, where each entry in the dictionary is numbered. The compressed data contains the dictionary plus a sequence of numbers which represent the occurrence of the sequences in the original text. On standard text, this typically enables 10:1 compression.
** Decomposition
*** Compound audio wavforms can be decomposed into individual signals, which can then be modelled as repeated sequences. For example, a waveform consisting of two notes being played at different frequencies can be decomposed into those separate notes; since each note consists of a number of repetitions of a particular wave pattern, they can individually be represented in a more compact format by describing the frequency, waveform shape, and amplitude characteristics.
** Pallettization
*** Images often contain repeated colours, and rarely use all of the available colours in the original encoding scheme. For example, a 1920x1080 image contains about 2 million pixels, so if every pixel was a different colour, there would be a maximum of 2 million colours. But it's likely that many of the pixels in the image are the same colour, so there might only be (perhaps) 4000 colours in the image. If each pixel is encoded as a 24-bit value, there are potentially 16 million colours available, and there is no possibility that they are all used. Instead, a palette can be provided which specifies each of the 4000 colours used in the picture, and then each pixel can be encoded as a 12-bit number which selects one of the colours from the palette. The total storage requirement for the original 24-bit scheme is 1920*1080*3 bytes per pixel = 5.9 MB. Using a 12-bit pallette, the storage requirement is 3 * 4096 bytes for the palette plus 1920*1080*1.5 bytes for the image, for a total of 3 MB -- a reduction of almost 50%
** Psychoacoustic and psychovisual compression
*** Much of the data in sound and images cannot be perceived by humans. Psychoacoustic and psychovisual compression remove artifacts which are least likely to be perceived. As a simple example, if two pixels on opposite sides of a large image are almost but not exactly the same, most people won't be able to tell the difference, so these can be encoded as the same colour if that saves space (for example, by reducing the size of the colour palette).
=== Week 1 Deliverables ===
