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Data Storage – Part 1

Data Storage – Part 1. CS 1 Introduction to Computers and Computer Technology Rick Graziani Fall 2013. BIT – BI nary digi T. Bit (Binary Digit) = Basic unit of information, representing one of two discrete states . The smallest unit of information within the computer.

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Data Storage – Part 1

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  1. Data Storage – Part 1 CS 1 Introduction to Computers and Computer Technology Rick Graziani Fall 2013

  2. BIT – BInary digiT • Bit (Binary Digit) = Basic unit of information, representing one of two discrete states. The smallest unit of information within the computer. • The only thing a computer understands. • Abbreviation: b • Bit has one of two values: • 0 (off) or 1 (on) • 0 (False) or 1 (True) ON OFF Rick Graziani graziani@cabrillo.edu

  3. Bits • Two patterns are known as the state of the bit. • For example, magnetic encoding of information on tapes, floppy disks, and hard disks are done with positive or negative polarity. The boxes illustrate a position where magnetism may be set and sensed; pluses (red) indicate magnetism of positive polarity (1 bit), interpreted as “present” and minuses (blue) (0 bit). 0 1 1 0 1 0 0 0 1 0 1 1 0 1 0 1 Rick Graziani graziani@cabrillo.edu

  4. Bits • Bits are really only symbols. • Used to display the one of two different, discrete states. • Bits are used as: • Storing data • Numbers • Text characters • Images • Sound • Etc. • Processing data Rick Graziani graziani@cabrillo.edu

  5. Boolean Operations • Integrated Circuits (microchips) are used to store and manipulate (process) bits. • This is done using Boolean operations (in honor of mathematician George Boole, 1815-1864). • Boolean Operation: An operation that manipulates one or more true/false values • Specific operations • AND • OR • XOR (exclusive or) • NOT • Using Truth Tables we can uses different sets of logic operations to store, add, subtract, and more complicated operations with bit. Rick Graziani graziani@cabrillo.edu

  6. Boolean Algebra and logical expressions (Addendum) • Boolean algebra (due to George Boole) - The mathematics of digital logic • Useful in dealing with binary system of numbers. • Used in the analysis and synthesis of logical expressions. • Logical expressions– Expressions constructed using logical-variables and operators. • Result is: True or False • Boolean algebra – In mathematics a variable uses one of the two possible values: 1 or 0 • May also be represented as: • Truth or Falsehood of a statement • On or Off states of a switch • High (5V) or low (0V) of a voltage level Rick Graziani graziani@cabrillo.edu

  7. Used in electronics (Addendum) • Electrical circuits aredesigned to represent logical expressions • Known as logic circuits. • Used to make important logical decisions in household appliances, computers, communication devices, traffic signals and microprocessors. • Three basic logic operations as listed below: • OR operation • AND operation • NOT operation • A logic gate is an electronic circuit/device which makes the logical decisions based on these operations. Rick Graziani graziani@cabrillo.edu

  8. Logic gates (Addendum) • Logic gates have: • one or more inputs • only one output • The output is active only for certain input combinations. • Logic gates are the building blocks of any digital circuit. Rick Graziani graziani@cabrillo.edu

  9. Boolean Operations - AND • Truth tables (simple ones) • AND operation • Both input values must be TRUE for output to be TRUE • Kermit is a frog AND Miss Piggy is an actress • Inputs to AND operation represent truth of falseness of the compound statement. TRUE TRUE AND = TRUE Rick Graziani graziani@cabrillo.edu

  10. Boolean Operations • Gate: • A device that computes a Boolean operation • A device that produces the output of a Boolean operation when given the operation’s input values. • Gates can be: • Gears • Relays • Optic devices • Electronic circuits (microchips) Rick Graziani graziani@cabrillo.edu

  11. Boolean Operations – AND Gate 0 = FALSE 1 = TRUE AND operation • Both input values must be TRUE for output to be TRUE 0 Truth Table 0 InputsOutput 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 1 1 Rick Graziani graziani@cabrillo.edu

  12. Boolean Operations - OR TRUE • Truth tables (simple ones) • OR operation • Only one input values must be TRUE for output to be TRUE • In Rick likes to surf OR Rick likes to go dancing. • Taking both courses will also TRUE. OR True = TRUE Rick Graziani graziani@cabrillo.edu

  13. Boolean Operations – OR Gate 0 = FALSE 1 = TRUE OR operation • At least one input value must be TRUE for output to be TRUE 0 Truth Table 0 InputsOutput 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 Rick Graziani graziani@cabrillo.edu

  14. Boolean Operations - XOR TRUE • Truth tables (simple ones) • XOR operation • One and ONLY one input value can be TRUE for output to be TRUE • At noon Rick is going to surf the Hook XOR surf Liquor Stores (this is a surf spot) • Both cannot be true, as I cannot surf both spots at the same time. XOR False = TRUE Rick Graziani graziani@cabrillo.edu

  15. Boolean Operations – XOR Gate 0 = FALSE 1 = TRUE XOR operation • Only one input value is TRUE for output to be TRUE 0 Truth Table 0 InputsOutput 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 1 0 1 0 1 Rick Graziani graziani@cabrillo.edu

  16. Boolean Operations – NOT Gate 0 = FALSE 1 = TRUE NOT operation • Only one input • Opposite of input NOT FALSE = TRUE NOT TRUE = FALSE Truth Table 0 1 InputsOutput 0 1 1 0 1 0 Rick Graziani graziani@cabrillo.edu

  17. http://www.cs.kent.edu/~volkert/F10-10051/notes/logsim.html Rick Graziani graziani@cabrillo.edu

  18. Another way to write it… 0 = FALSE; 1 = TRUE Rick Graziani graziani@cabrillo.edu

  19. Binary Math Rick Graziani graziani@cabrillo.edu

  20. Base 10 (Decimal) Number System Digits (10): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Number of: 104 103 102 101 100 10,000’s1,000’s100’s10’s1’s 1 2 3 9 1 0 9 9 1 0 0 Rick Graziani graziani@cabrillo.edu

  21. Base 10 (Decimal) Number System Digits (10): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Number of: 104 103 102 101 100 10,000’s1,000’s100’s10’s1’s 4 1 0 8 3 8 2 1 0 0 0 9 1 0 0 1 0 Rick Graziani graziani@cabrillo.edu

  22. Rick’s Number System Rules • All digits start with 0 • A Base-n number system has n number of digits: • Decimal: Base-10 has 10 digits • Binary: Base-2 has 2 digits • Hexadecimal: Base-16 has 16 digits • The first column is always the number of 1’s • Each of the following columns is n times the previous column (n = Base-n) • Base 10: 10,000 1,000 100 10 1 • Base 2: 16 8 4 2 1 • Base 16: 65,536 4,096 256 16 1 Rick Graziani graziani@cabrillo.edu

  23. Counting in Decimal (0,1,2,3,4,5,6,7,8,9) 1,000’s100’s10’s1’s 0 1 2 3 ... 9 1 0 1 1 ... 1 8 1 9 2 0 2 1 2 2 1,000’s100’s10’s1’s . . . 2 9 3 0 3 1 ... 9 9 1 0 0 1 0 1 ... 9 9 9 1 0 0 0 Rick Graziani graziani@cabrillo.edu

  24. Counting in Binary (0, 1) 8’s4’s2’s1’s 0 1 1 0 1 1 1 0 0 1 0 1 Dec 8’s4’s 2’s1’s Dec 0 9 1 0 0 1 1 10 1 0 1 0 2 3 1 0 1 1 11 4 12 1 1 0 0 5 1 1 0 6 1 1 0 1 13 1 1 1 7 1 1 1 0 14 1 0 0 0 8 1 1 1 1 15 Rick Graziani graziani@cabrillo.edu

  25. Binary Math (more later) 0 0 1 10 11 100 101 +0 +1 +1 +1 +1 + 1 + 1 0 1 10 11 100 101 110 111 00000000 11111110 + 1 + 0 -> + 1 1000 …… 00000000 11111111 Rick Graziani graziani@cabrillo.edu

  26. Base 2 (Binary) Number System Digits (2): 0, 1 Number of: 27 26 25 24 23 22 21 20 128’s64’s32’s16’s8’s4’s2’s1’s Dec. 2 1 0 10 1 0 1 0 17 70 130 255 Rick Graziani graziani@cabrillo.edu

  27. Base 2 (Binary) Number System Digits (2): 0, 1 Number of: 27 26 25 24 23 22 21 20 128’s64’s32’s16’s8’s4’s2’s1’s Dec. 2 1 0 10 1 0 1 0 17 1 0 0 0 1 70 1 0 0 0 1 1 0 130 1 0 0 0 0 0 1 0 255 1 1 1 1 1 1 1 1 Rick Graziani graziani@cabrillo.edu

  28. Converting between Decimal and Binary Digits (2): 0, 1 Number of: 27 26 25 24 23 22 21 20 128’s64’s32’s16’s8’s4’s2’s1’s Dec. 1 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 172 192 Rick Graziani graziani@cabrillo.edu

  29. Converting between Decimal and Binary Digits (2): 0, 1 Number of: 27 26 25 24 23 22 21 20 128’s64’s32’s16’s8’s4’s2’s1’s Dec. 70 1 0 0 0 1 1 0 40 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 128 1 0 0 0 0 0 0 0 172 1 0 1 0 1 1 0 0 192 1 1 0 0 0 0 0 0 Rick Graziani graziani@cabrillo.edu

  30. Computers do Binary 0 1 • Bits have two values: OFF and ON • The Binary number system (Base-2) can represent OFF and ON very well since it has two values, 0 and 1 • 0 = OFF • 1 = ON • Understanding Binary to Decimal conversion is critical in computer science, computer networking, digital media, etc. Rick Graziani graziani@cabrillo.edu

  31. Rick’s Program Rick Graziani graziani@cabrillo.edu

  32. Rick’s Program Rick Graziani graziani@cabrillo.edu

  33. Rick’s Program Rick Graziani graziani@cabrillo.edu

  34. Decimal Math - Addition 10,000’s1,000’s100’s10’s1’s 1 6 5 1 0 + 1 6 5 9 5 ----------------------------- 1 1 1 3 3 1 0 5 Rick Graziani graziani@cabrillo.edu

  35. Binary Math - Addition 64’s32’s16’s8’s4’s2’s1’s 1 1 1 0 1 0 + 1 1 0 1 1 ----------------------------- Dec 1 1 1 1 58 + 27 ----- 1 0 1 0 1 0 1 85 Double check using Decimal. Rick Graziani graziani@cabrillo.edu

  36. Half Adder Gate – Adding two bits Inputs: A, B S = Sum C = Carry XOR AND A + B = 2’s1’s Rick Graziani graziani@cabrillo.edu

  37. Half Adder Gate – Adding two bits Inputs: A, B S = Sum C = Carry XOR 0 0 0 0 AND C S 0 + 0 ---- A + B = 2’s1’s 0 0 = 0 0 0 Rick Graziani graziani@cabrillo.edu

  38. Half Adder Gate – Adding two bits Inputs: A, B S = Sum C = Carry XOR 0 1 1 0 AND C S 0 + 1 ---- A + B = 2’s1’s 0 1 = 0 1 1 Rick Graziani graziani@cabrillo.edu

  39. Half Adder Gate – Adding two bits Inputs: A, B S = Sum C = Carry XOR 1 1 0 0 AND C S 1 + 0 ---- A + B = 2’s1’s 1 0 = 0 1 1 Rick Graziani graziani@cabrillo.edu

  40. Half Adder Gate – Adding two bits Inputs: A, B S = Sum C = Carry XOR 1 0 1 1 AND C S 1 + 1 ---- A + B = 2’s1’s 1 1 = 1 0 1 0 Rick Graziani graziani@cabrillo.edu

  41. Marble Adding Machine • http://www.youtube.com/watch?v=GcDshWmhF4A&NR=1&feature=fvwp Rick Graziani graziani@cabrillo.edu

  42. Flip-flops • Flip-flop: A circuit built from gates that can store one bit, uses feedback. • A means of storing bits such as RAM • Modern computers use technologies with: • greater miniaturization • faster response times • additional circuitry • DRAM (Dynamic RAM) • SDRAM (Synchronous DRAM) • PCs currently use DDR (double data rate) for RAM, DDR1, DDR2 and DDR3 • Type of SDRAM • Each type has types of DIMM (dual in-line memory module) slots (different number of pins) Rick Graziani graziani@cabrillo.edu

  43. Example of Flip Flops storing bits (FYI) • S = Set • R = Reset • DRAM (Dynamic RAM) • Each bit of data is stored in a separate capacitor within an integrated circuit. • Since real capacitors leak charge, the information eventually fades unless the capacitor charge is refreshed periodically. Rick Graziani graziani@cabrillo.edu

  44. Types of RAM • Understanding RAM Types: DRAM, SDRAM, DIMM, SIMM & More • http://proprofs.com/mwiki/index.php?title=Understanding_RAM_Types:_DRAM_SDRAM_DIMM_SIMM_And_More • RAM - From Wikipedia, the free encyclopedia • http://en.wikipedia.org/wiki/RAM • DDR2 SDRAM - From Wikipedia, the free encyclopedia • http://en.wikipedia.org/wiki/DDR2_SDRAM • Dynamic random access memory - From Wikipedia, the free encyclopedia • http://en.wikipedia.org/wiki/Dynamic_random_access_memory Rick Graziani graziani@cabrillo.edu

  45. Data Storage – Part 1 CS 1 Introduction to Computers and Computer Technology Rick Graziani

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