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CSE 111

CSE 111. Information Representation in the Digital World. Analog vs. Digital. Faucet Example Consider a faucet Digital Water can be flowing or NOT flowing from the faucet Two States On Off Analog How much water is flowing from the faucet?

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CSE 111

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  1. CSE 111 Information Representation in the Digital World

  2. Analog vs. Digital • Faucet Example • Consider a faucet • Digital • Water can be flowing or NOT flowing from the faucet • Two States • On • Off • Analog • How much water is flowing from the faucet? • How many different answers can there be to this question?

  3. Analog vs. Digital • Faucet Example • Advantages of Digital • Replication • Analog • Try replicating the exact flow from a faucet • Digital • Try replicating ON or OFF

  4. Analog vs. Digital • Advantages of Digital Circuits • Replication • Error Correction/Detection • Small errors don’t propagate • Miniturization of Circuits • Programmability • Digital computers are programmable

  5. The Digital System • Two discrete values are used in digital systems. • How are discrete elements represented? • Signals are the physical quantities used to represent discrete elements of information in a digital system. • Electric signals used: • Voltage • Current

  6. The Digital System • Representation of Binary Values

  7. The Digital System • Representation of Binary Values • Why are there voltage ranges instead of exact voltages? • Variations in circuit behavior & noise

  8. The Binary System • Why use binary? • Natural Choice • A switch can be ‘on’ or ‘off’ • Two states • Binary has two symbols, 1 and 0 • A transistor is an automated, electrically controlled switch

  9. The Bit • The smallest unit that can represent information • Binary Digit • Two possible values • 1, 0 • On, Off • True, False • High, Low • Heads, Tails • Black, White

  10. How many bits does it take? • One bit can represent two numbers (0, 1) • 21 = 2 • Two bits can represent four numbers (00, 01, 10, 11) • 22 = 4 • Three bits can represent eight numbers (000, 001, 010, 011, 100, 101, 110, 111) • 23 = 8 • Four bits can represent how many numbers? • 24 = 16 • Ten bits can represent how many numbers? • 210=1,024 • 64 bits can represent how many numbers? • 264=18,446,744,073,709,551,616 • Note the importance of the math! • You’re NOT going to enumerate all possible combinations and count them to answer this question!

  11. Bits & Bytes • Nibble • 4 bits • Older term, not widely used today • Byte • 8 bits • Word • The number of bits a microprocessor can process at a single time • Most of today’s processor have a 32-bit word size • 64-bit is quickly becoming the norm

  12. Data Representation • Bits are grouped to represent both data and instructions in a digital system • Coding Techniques • Defines how bits are grouped together to represent information • Types • Numeric • Character • Error Detection/Correction

  13. References • Donald D. Givone, Digital Principles and Design, McGraw-Hill, 2003

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