Week 2 - Digital Data Representation PDF

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Digital Data Representation...

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Computer Architecture Week 2 - Digital Data Representation Digital representation - When you order something at Tim Hortons the machine/computer has to calculate your total amount Numbering Systems: Decimal System o As human beings, we use (decimal) numbering system o Base 10 (0-9) - Binary System o Computers use -- from the on/off switch o binary Base2 (0 and 1) - Hexadecimal System o Hex base 16 (0-15) o Also add A, B, C, D, E, F - Octal System o Octal base 8 (0-7)  Used in CHMOD 777 - Unary System o UNARY base1  1, 11, 111, 1111, 1111  how elementary school kids learned to add **will be getting a reference sheet for the exam ** max number without a calculator (so for an exam) the highest number will be decimal 999 -

Decimal to Binary

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Method 1: Successive Division by 2 o Bottom to top (referring from table) o Can make mistakes with this method o Takes a long time

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Method 2: The Powers of 2

Binary to Decimal

Binary to Hexadecimal - Method: Hexadecimal o Divide by 16 o To make it easier convert the decimal number to binary and then convert to Hexadecimal  This way you don’t have to divide by 16 o From right to lef

Digital Data Representations - Computers can store and work with many different kinds of information - Numbers (integers) o Signed integers  Whole numbers plus negative numbers  Two ways to represent signed integers:  Sign-magnitude o Your first bit (lef most bit) o 8-bit representation (byte)  Two’s compliment (-128 to 127)  -2(n-2) to 2(n-1) - 2 o Most commonly used in computers o First convert the number to binary o Flip all zeros into 1 and 1’s into zeros (flip bits)  0000 0001  1111 1110 o add 1  1111 1111 o (use minimum of 8 bits) o works for negative numbers  **if the number is Positive only do step 1!!!!! o Unsigned integers  Whole numbers: Only zero and positive numbers  Range: 0 - 255 Non-numeric Data Types - Text - Images o Still and moving o Images use a dot or a pixel o Images get stored in a computer’s memory as numbers o Each number represents a dot or pixel of the image o Also uses colour  RGB - Movies o Moving images o Sequence of still images called frames - Music/audio o Represented as a sequence of numbers in computer memory o Ofen stored in compressed formats  MP3, AAC, FLAC - Therefore, the CPU must be able to work with this data

Data Compression - Images, audio, and video data take up a lot of memory or disk space unless it is compressed - Two types of compression o Lossless  Reduces the size of data without losing or changing any information (data)

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 Lossy  

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The result is a stream of bytes that can be stored in memory, saved in a disk file, or transmitted over the internet Decompression restores the original data EXACTLY for example:  ZIP files Compression Ratio  Describes the effectiveness of the compression method  Ratio of 2:1  the compressed data is half the original size  Ratio of 10:1  means one tenth of the original size  Ratio of 1:1  no reduction in size **Unfortunately, lossless type does not work very well for video and audio data Change or discard some of the data in a way that is hard for the human senses to notice Compression ratios can be impressively high  Typical ratio for JPEG: 10:1 or 20:1  Typical ratio for MP2/ACC music are about 10:1  MPEG-4 video compression ratio: 100:1 to 200:1 The algorithm usually includes an encoding quality or bit rate parameter  Higher quality  lower compression ratio (higher bit rate)  Lower quality  higher compression ratio (lower bit rate) Effects of lower quality?  Blocky or grainy images/video  Music: unclear high end (“sizzle”), less stereo separation, distortion...