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Exploring Low-Level Components: Decoders and Their Application in Circuits

This lecture focuses on low-level components such as multiplexers, demultiplexers, and decoders with a particular emphasis on the implementation of the majority function using decoders. Key concepts include minterms and maxterms, Karnaugh maps, and designing circuits that connect inputs and outputs through these components. The session also covers practical steps for building a circuit for a clock radio, exploring the relationship between inputs and outputs, and the use of truth tables for developing Boolean equations. Logisim demonstrations will illustrate the application of these theories.

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Exploring Low-Level Components: Decoders and Their Application in Circuits

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  1. ITEC 352 Lecture 5 Low level components(3)

  2. Review • Multiplexers • Demultiplexer • Minterm/Maxterm • Karnaugh Map

  3. Outline • Decoders • 7 Segment display

  4. Decoder • Similar to a DeMultiplexer • Essential difference: the select (or control lines) are now considered as part of input. • Used to convert logical encoding into spatial encoding. • Decoders generate the minterms for a function.

  5. A 2-4 Decoder: generates all possible minterms with 2 bits

  6. Majority Function • Implement it using a decoder

  7. Using a Decoder to Implement the Majority Function

  8. Example decoder • Example:Develop a circuit for this: • Develop a circuit that drives one input digit for this clock radio.

  9. Clock radio • Step 1: • Initial questions: • How many outputs are there for the circuit ? • How many inputs are needed to design this circuit ? • Usually we are interested only in the minimum number of inputs. • However, sometimes it helps us look at other inputs. • What possible other inputs can you think of ? • Next: How are the outputs related to the inputs.

  10. numeric display (2) • How are the outputs related to the inputs ? • Capture this function using a boolean equation • How do we derive boolean equations? use truth tables. a b f g e c d

  11. numeric display (3) • Draw the truth table for matching inputs to outputs.

  12. numeric display (4) • Which of the following standard circuits can you use to develop this circuit: • Decoder • Multiplexer • Demultiplexer • Why ?

  13. numeric display (5) • Decoders generate minterms. • What type of a decoder would you use: • 1 X 2 • 2 X 4 • 3 X 8 • Etc.. ?

  14. Implementation • Logisim demonstration

  15. Review • Decoders • Majority function

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