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Understanding Digital Systems: Analog vs. Digital Representation

Learn about analog vs. digital representation using the faucet example and how binary values are used in digital systems. Explore the advantages of digital circuits, data representation, bits and bytes, and coding techniques. References: Donald D. Givone's "Digital Principles and Design."

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Understanding Digital Systems: Analog vs. Digital Representation

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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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