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ECE 331 – Digital System Design

Basic Logic Operations and Standard Logic Gates (Lecture #1). ECE 331 – Digital System Design. What is an analog signal?. Analog Signal. An analog signal is a signal that can take on a continuous range of values. Analog Signal.

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ECE 331 – Digital System Design

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  1. Basic Logic Operations and Standard Logic Gates (Lecture #1) ECE 331 – Digital System Design

  2. ECE 331 - Digital Systems Design What is an analog signal?

  3. ECE 331 - Digital Systems Design Analog Signal • An analog signal is a signal that can take on a continuous range of values.

  4. ECE 331 - Digital Systems Design Analog Signal • Most, if not all, physical (naturally occurring) quantities are analog values. • Time • Temperature • Pressure

  5. ECE 331 - Digital Systems Design What is an digital signal?

  6. ECE 331 - Digital Systems Design Digital Signal • An digital signal is a signal that can take on only discrete (specific) values.

  7. ECE 331 - Digital Systems Design What is an binary signal?

  8. ECE 331 - Digital Systems Design Binary Signal • An binary signal is a signal that can take on only two values. • Typically represented by 0 and 1.

  9. ECE 331 - Digital Systems Design Can a binary number be used to represent an analog value? What about accuracy (or is it precision)?

  10. ECE 331 - Digital Systems Design Can a binary number be used to represent an digital value? How many bits are required?

  11. ECE 331 - Digital Systems Design Sample and Hold ADC Binary Encoder analog sampled digital binary Processing Physical Quantities • The analog signal (representing the physical quantity) must be sampled at specific instances in time. • The sampled values must be digitized. • The digital value must be encoded in binary.

  12. ECE 331 - Digital Systems Design Basic Logic Operations

  13. ECE 331 - Digital Systems Design Definition: the output is true (1) iff both inputs are true (1). AND logical operator F = A.B = AB = “A and B” Boolean expression F Truth table Symbol (aka. logic gate)

  14. ECE 331 - Digital Systems Design Definition: the output is true (1) if either or both inputs are true (1). F F OR logical operator F = A+B = “A or B” Boolean expression Truth table Symbol

  15. ECE 331 - Digital Systems Design Definition: the output is true (1) if the input is false (0). NOT logical operator F = A' = “ not A” Boolean expression Truth table A F = A' Symbol

  16. ECE 331 - Digital Systems Design Order of Precedence • The order of precedence of the basic logic operations is defined as follows: • NOT • AND • OR • The order of precedence can be modified by using parenthesis.

  17. ECE 331 - Digital Systems Design Functionally Complete • The AND, OR, and NOT operations comprise a functionally complete set. • All logic functions can be expressed in terms of these logic operations. • All logic circuits can be realized using the associated logic gates.

  18. ECE 331 - Digital Systems Design Definition: the output is false (0) iff both inputs are true (1). NAND F = (A.B)' = “not (A and B)” Boolean expression F = (A.B)' Truth table Symbol shorthand for inversion

  19. ECE 331 - Digital Systems Design Definition: the output is false (0) if either or both inputs are true (1). F F NOR F = (A+B)' = “not (A or B)” Boolean expression F = (A+B)' F Truth table Symbol shorthand for inversion

  20. ECE 331 - Digital Systems Design Definition: the output is true (1) if either but not both inputs are true (1). XOR F = A xor B Boolean expression logical operator Truth table Symbol

  21. ECE 331 - Digital Systems Design Definition: the output is false (0) if either but not both inputs are true (1). XNOR (aka. Equivalence) F = A xnor B Boolean expression logical operator Symbol Truth table

  22. ECE 331 - Digital Systems Design Logic Circuits • Logic circuits are realized through the interconnection of logic gates. • Each logic gate represents a logical operation. • This can be done using • discrete components • Standard Logic Gates • programmable devices • Read-only Memories (ROM) • Programmable Logic Devices (PLD) • Field Programmable Gate Arrays (FPGA)

  23. ECE 331 - Digital Systems Design Standard Logic Gates

  24. ECE 331 - Digital Systems Design Standard Logic Gates Note: “xx” refers to the logic family

  25. ECE 331 - Digital Systems Design Standard Logic Gates • Data sheets provide essential information: • Logic Function • Truth Table • Pin-out • Electrical Characteristics • Timing Characteristics • Package Description(s) • This information is necessary when building logic circuits from discrete components. • Each logic family has a unique set of characteristics.

  26. ECE 331 - Digital Systems Design Standard Logic Gates: 74xx08 pin-out Truth table

  27. ECE 331 - Digital Systems Design Standard Logic Gates: 74xx32 pin-out Truth table

  28. ECE 331 - Digital Systems Design Standard Logic Gates: 74xx04 pin-out Truth table

  29. ECE 331 - Digital Systems Design C B inputs output F A Building a Logic Circuit Circuit Diagram 74xx08 74xx04 74xx32 74xx08 Boolean Expression F = B'.C + A.B

  30. ECE 331 - Digital Systems Design V DD 7404 7408 7432 A B C F Building a Logic Circuit Wiring Diagram components wires inputs output

  31. ECE 331 - Digital Systems Design Draw the circuit diagram and wiring diagram for the following Boolean expression: F = A'.B + A.B' Example

  32. ECE 331 - Digital Systems Design Example (circuit diagram)

  33. ECE 331 - Digital Systems Design Example

  34. ECE 331 - Digital Systems Design Questions?

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