Chapter 8_1 Bits and the "Why" of Bytes: Representing Information Digitally
Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 8-2
Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 8-3 Digitizing Discrete Information Digitize: Represent information with digits (numerals 0 through 9) Limitation of Digits –Alternative Representation: Any set of symbols could represent phone number digits, as long as the keypad is labeled accordingly Symbols, Briefly –Digits have the advantage of having short names (easy to say) But computer professionals are shortening symbol names (exclamation point is pronounced "bang")
Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 8-4 Ordering Symbols Advantage of digits for encoding info is that items can be listed in numerical order To use other symbols, we need an ordering system (collating sequence) –Agreed order from smallest to largest value In choosing symbols for encoding, consider how symbols interact with things being encoded
Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 8-5 Encoding with Dice Consider a representation based on dice –Single die has six sides, and the patterns on the sides can be used for digital representation
Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 8-6 Encoding with Dice (cont'd) Consider representing the Roman alphabet with dice –26 letter, only 6 patterns on a die –We use multiple patterns to represent each letter –How many patterns are required? 2 dice can produce 36 pattern sequences (6*6) 3 dice can produce 216 (6*6*6) n dice can produce 6 n sequences
Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 8-7 Encoding with Dice (cont'd)
Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 8-8 Encoding with Dice (cont'd) Call each pattern produced by pairing two dice a symbol: –1 and 1 == A –1 and 2 == B –1 and 3 == C –1 and 4 == D –1 and 5 == E –1 and 6 == F –2 and 1 == G –etc.
Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 8-9 Encoding with Dice (cont'd)
Copyright © 2006 Pearson Addison-Wesley. All rights reserved Extending the Encoding 26 letters of the Roman alphabet are represented; 10 spaces are blank These spaces can be used for the Arabic numerals What is we need punctuation? We only have 36 available spaces in the two-dice system. How can we avoid going to a three-dice system?
Copyright © 2006 Pearson Addison-Wesley. All rights reserved The Escape: Creating More Symbols We can use the last two-dice symbol as "escape". It does not match any legal character, so it will never be needed for normal text digitization It indicates that the digitization is "escaping from the basic representation" and applying a secondary representation We could also use a "double escape" to enter a tertiary representation system
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Copyright © 2006 Pearson Addison-Wesley. All rights reserved The Fundamental Representation of Information The fundamental patters used in IT come when the physical world meets the logical world The most fundamental form of information is the presence or absence of a physical phenomenon In the logical world, the concepts or true and false are important –By associating true with the presence of a phenomenon and false with its absence, we use the physical world to implement the logical world, and produce information technology
Copyright © 2006 Pearson Addison-Wesley. All rights reserved The PandA Representation PandA is the mnemonic for "presence and absence" It is discrete (distinct or separable)—the phenomenon is present or it is not (true or false). There in no continuous gradation in between
Copyright © 2006 Pearson Addison-Wesley. All rights reserved A Binary System Two patterns—Present and Absent— make PandA a binary system We can give any names to these two patterns as long as we are consistent The PandA basic unit is known as a "bit" (short for binary digit)
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Copyright © 2006 Pearson Addison-Wesley. All rights reserved Bits in Computer Memory Memory is arranged inside a computer in a very long sequence of bits (places where a phenomenon can be set and detected) Analogy: Sidewalk Memory –Each sidewalk square represents a memory slot, and stones represent the presence or absence –If a stone is on the square, the value is 1, if not the value is 0
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Copyright © 2006 Pearson Addison-Wesley. All rights reserved Units of Data Measures the size or volume of data BIT:Single binary digit, either a 1 or a 0 BYTE:A group of eight bits, a character (Basic unit for measuring the size of the data) KILOBYTE:2 10 or 1024 bytes (not 1000 used in scientific notation for the prefix kilo) MEGABYTE: 2 20 or 1,048,576 bytes (not used in scientific notation for the prefix mega-) WORD: the number of adjacent bits that are manipulated or stored as a unit in a particular computer system
Copyright © 2006 Pearson Addison-Wesley. All rights reserved Alternative PandA Encodings There are other ways to encode two states using physical phenomena –Use stones on all squares, but black stones for one state and white for the other –Use multiple stones of two colors per square, saying more black than white means 0 and more white than black means 1 –Stone in center for one state, off-center for the other –etc.
Copyright © 2006 Pearson Addison-Wesley. All rights reserved Combining Bit Patterns Since we only have two patterns, we must combine them into sequences to create enough symbols to encode necessary information PandA has p=2 patterns, arranging them into n-length sequences, we can create 2 n symbols
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Copyright © 2006 Pearson Addison-Wesley. All rights reserved Hex Explained Recall in Chapter 4, we specified custom colors in HTML using hex digits –e.g., –Hex is short for hexadecimal, base 16 Why use hex? Writing the sequence of bits is long, tedious, and error-prone
Copyright © 2006 Pearson Addison-Wesley. All rights reserved The 16 Hex Digits 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F Sixteen digits (or hexits) can be represented perfectly by the 16 symbols of 4-bit sequences Changing hex digits to bits and back again: –Given a sequence of bits, group them in 4's and write the corresponding hex digit –Given hex, write the associated group of 4 digits
Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 8-25
Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 8-26
Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 8-27