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ECE 331 – Digital System Design

Basic Logic Functions, Truth Tables, and Standard Logic Gates. ECE 331 – Digital System Design. Basic Logic Functions. Basic Logic Functions. AND Logical multiplication (product) A . B = AB = “A and B” OR Logical addition (sum) A + B = “A or B” NOT Logical complement A‘ = “not A”.

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ECE 331 – Digital System Design

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  1. Basic Logic Functions, Truth Tables, and Standard Logic Gates ECE 331 – Digital System Design

  2. ECE 331 - Digital System Design Basic Logic Functions

  3. ECE 331 - Digital System Design Basic Logic Functions • AND • Logical multiplication (product) • A . B = AB = “A and B” • OR • Logical addition (sum) • A + B = “A or B” • NOT • Logical complement • A‘ = “not A” Order of Precedence: 1. NOT 2. AND 3. OR - can be modified by parenthesis

  4. ECE 331 - Digital System Design Truth Table

  5. ECE 331 - Digital System Design x 1 x 2 x 1     x x x  x x 1 2 n 1 2 x 2 x n (a) AND gates x 1 x 2 x 1  x + x x + x + + x 1 2 1 2 n x 2 x n (b) OR gates x x (c) NOT gate Logic Gates

  6. ECE 331 - Digital System Design Additional Logic Functions • NAND • F = (A . B)‘ = (AB)’ • F = not (A and B) • Compound logic function • NOR • F = (A + B)’ • F = not (A or B) • Compound logic function Not the same as F = A’ . B’ Not the same as F = A’ + B’

  7. ECE 331 - Digital System Design Exercise: Derive the Truth Table for the NAND and NOR gates. Truth Tables

  8. ECE 331 - Digital System Design Logic Gates shorthand for a NOT gate

  9. ECE 331 - Digital System Design Additional Logic Functions • Exclusive-OR • F = (A.B') + (A'.B) • Output = 1 iff one of the inputs is 1 (but not both). • Inclusive-OR: F = A + B • Exclusive-NOR • F = (A.B) + (A'.B') • Output = 1 iff both input are 0 or both inputs are 1. • Also known as the Equivalence function.

  10. ECE 331 - Digital System Design Exercise: Derive the Truth Table for the XOR and XNOR gates. Truth Tables

  11. ECE 331 - Digital System Design A B XOR gate F = A xor B F = A xnor B XNOR gate Additional Logic Operations

  12. ECE 331 - Digital System Design Truth Tables

  13. ECE 331 - Digital System Design Truth Tables • Used to describe the functional behavior of a Boolean expression and/or Logic circuit. • Each row in the truth table represents a unique combination of the input variables. • For n input variables, there are 2n rows. • The output of the logic function is defined for each row. • Each row is assigned a numerical value, with the rows listed in ascending order. • The order of the input variables defined in the logic function is important.

  14. ECE 331 - Digital System Design 3-input Truth Table

  15. ECE 331 - Digital System Design 4-input Truth Table

  16. ECE 331 - Digital System Design Standard Logic Gates

  17. ECE 331 - Digital System Design Standard Logic Gates • Discrete components used to build logic circuits. • 74xx08 AND gate • 74xx32 OR gate • 74xx04 NOT gate • 74xx00 NAND gate • 74xx02 NOR gate • 74xx86 XOR gate • Logic Families (TTL, LS-TTL, F, HC)

  18. ECE 331 - Digital System Design Standard Logic Gates: Data sheets • 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.

  19. ECE 331 - Digital System Design Logic Families • TTL • Low-Power TTL (“L”) • High-Speed TTL (“H”) • Schottky (“S”) • Low-Power Schottky (“LS”) • Advanced Schottky (“AS”) • Advanced Low-Power Schottky (“ALS”) • Fast (“F”) • CMOS • High-Speed CMOS (“HC”) • Advanced CMOS (“AC”)

  20. ECE 331 - Digital System Design Table E.4 (p. 916 of textbook)

  21. ECE 331 - Digital System Design Combinational Logic Circuits

  22. ECE 331 - Digital System Design Combinational Logic Circuits • Composed of an interconnected set of logic gates. • Also known as Switching Circuits • Logic circuits can be designed from • Truth tables • Boolean expressions • Logic circuits realized through • Interconnection of discrete components • Synthesis from a Hardware Description Language

  23. ECE 331 - Digital System Design Example: Derive the Boolean expression and draw the circuit diagram for the following truth table:

  24. ECE 331 - Digital System Design x 1 x 2 f Example F = x’1.x’2 + x’1.x2 + x1.x2

  25. ECE 331 - Digital System Design Example: Derive the Boolean expression and draw the circuit diagram for the following truth table:

  26. ECE 331 - Digital System Design Wiring Diagrams

  27. ECE 331 - Digital System Design (a) Dual-inline package V DD Gnd (b) Structure of 7404 chip Standard Logic Gate: Pin-out

  28. ECE 331 - Digital System Design Standard Logic Gate: Pin-out

  29. ECE 331 - Digital System Design Standard Logic Gate: Pin-out

  30. ECE 331 - Digital System Design Example: Draw the circuit diagram and the wiring diagram for the following Boolean expression: F = x’2.x3 + x1.x2

  31. ECE 331 - Digital System Design V DD 7404 7408 7432 x 1 x 2 x 3 f Example

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