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Introduction to Digital Logic and Computer Organization

Explore gates, boolean algebra, logic circuits, memory elements, clocking, and more in this comprehensive guide to computer organization. Master digital logic circuits and understand the essentials of combinational logic systems. Dive into the world of transistors, truth tables, and two-level logic to build a solid foundation in computer organization. Delve into the basics of synchronous and combinatorial logic, and discover the power of multiplexers, decoders, and comparators in designing efficient systems.

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Introduction to Digital Logic and Computer Organization

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  1. CDA 3101 Spring 2016Introduction to Computer Organization Digital Logic “102” 12 Jan 2016 Mark Schmalz http://www.cise.ufl.edu/~mssz/CompOrg/Top-Level.html

  2. Overview • Review of gates and truth tables • Boolean algebra • Complex logic circuits • Combinational logic systems • Clocking • Memory elements

  3. Transistors Symbol Functional Behavior NOT gate (Inverter)

  4. Gate Symbol Truth Table NOT Gate NAND Gate

  5. AND, OR, NOR Gates NOR

  6. Boolean Algebra • Basic operators: OR (sum), AND (product), NOT • Boolean laws:

  7. Circuit Equivalence

  8. M = ABC + ABC + ABC + ABC The Majority Function M = f (A, B, C)

  9. M = ABC + ABC + ABC + ABC The Majority Function (cont’d) M = f (A, B, C) Step 1. Build truth table for logic function f. Step 2. Write logic equation in SOP form. 3b 1 1 0 3a Step 3.a) Build SOP circuit using minterms (M=1); b) OR minterms

  10. Combinatorial Logic • Many inputs and many outputs • Outputs are uniquely determined by inputs • Absence of memory elements • Basic combinatorial circuits • Multiplexers • Demultiplexers • Decoders • Comparators

  11. Multiplexer 2n data inputs 1 data output n control inputs

  12. Decoder n data inputs 2n data outputs 3-to-8 decoder

  13. Comparator

  14. Two-Level Logic PLA 12 inputs 6 outputs x

  15. Clocks Clock period

  16. Edge-Triggered Clocking State Element 1 State Element 2 Combinational logic State Element Combinational logic

  17. NOR SR Latch State 0 State 1 S - set Inputs Outputs: Q and Q R - reset

  18. Clocked SR Latch

  19. Clocked D Latch D C Q

  20. D flip-flop D D Q D Q Q D latch D latch Q C C Q C Setup time D hold time C Q

  21. Conclusions • Digital logic – lowest level of CDA3101 worldview • Digital logic circuits • Made from building blocks (AND,OR,NOT,…) • Simple or Complex, Combinatorial • Synchronous (clocked) or Asynchronous • Know rules for Boolean Algebra Enjoy your week!!

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