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( THE CS 115: COMPUTING FOR SOCIO-TECHNO WEB REPRESENTATION OF TEXT, NUMBERS AND CODE TODAY Computer components Binary numbers Text representation LOOKING UNDER THE HOOD OPENING THE BLACK BOX COMPUTER ARCHITECTURE A SIMPLE COMPUTER Fetch the next instruction from memory Decode it Execute it REPEAT ad infinitum BINARY NUMBERS BITS: 0 AND 1 The “blood” of the computer Only 2 bits: electric current passes or does not through a wire. Only 2 bits: we use symbols 0 and 1 Still enough to represent anything: • • • • Numbers Letters Instructions Images, videos, music, … Unbelievable? Amazing? OUR POSITIONAL DECIMAL SYSTEM • • • • • • Positional: The position of a digit has specific meaning. You know that 1492 = 1*1000 + 4*100 + 9*10 + 2*1 (duh!) We really mean 1492 = 1*103 + 4*102+ 9*101 + 2*100 (aha!) We really need a symbol for 0 in order to do that! The decimal system is great for arithmetic (if you are human) Computer use a binary system UNDERSTANDING POWERS OF 2 Like with our decimal system, we can represent any number in binary using powers of 2: • 1010 = 1*8 + 0*4 + 1*2 + 0*1 (= 10) • 1010 = 1*23 + 0*22 + 1*21 + 0*20 (= 10) The first 10 powers of 2: x 2x 1 2 2 4 3 8 4 16 5 32 6 64 7 128 8 256 9 512 10 1024 ANYWAY, IF YOU HAVE TWO SYMBOLS… Position of digit signifies contribution of (the corresponding) base power Base 10 • 1492 = 1*1000 + 4*100 + 9*10 + 2*1 • 2009 = 2*1000 + 0*100 + 0*10 + 9*1 Base 2: • 1010 = 1*8 + 0*4 + 1*2 + 0*1 (= 10) • 0111 = 0*8 + 1*4 + 1*2 + 1*1 (= 7) Activity: creating binary numbers You can represent any number! HOW MANY BITS DO YOU NEED? Bit depth Can repr. Bit depth 21 22 23 24 25 26 27 28 29 2 210 4 8 Byte ~ 101 220 16 32 230 64 128 256 512 Can represent up to… 1024 Kilobyte ~ 103 1,048,576 Megabyte ~ 106 1,073,741,824 Gigabyte ~ 109 QUANTITIES OF BYTES HAPPY BIRTHDAY TO ? 1100 11101110010 / 1001 / REPRESENTING TEXT … you can represent any character A is repr’d by 65, or 01000001 Hi! is repr’d by 72 105 33, or 010010000110100100100001 ASCII CODE HOW MANY ASCII CHARACTERS? 8 BITS EACH, SO THERE ARE IN ALL = 2 256 8 17 February 2, 2009 … OF ANY LANGUAGE THAT EXISTS OR EVER EXISTED UNICODE 20 HOW MANY UNICODE CHARACTERS? 32 BITS EACH, SO THERE ARE IN ALL 21 32 = 2 4,294,967,296