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Combinational Circuits

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Combinational Circuits

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    1. ELEE 4303 Combinational Circuits Concepts

    2. ELEE 4303 Outline Multiplexers Logic synthesis using multiplexers Shannon’s expansion Decoder Encoder BCD-to-7-segment display code converter

    3. ELEE 4303 2-to-1 multiplexer

    4. ELEE 4303 4-to-1 multiplexer

    5. ELEE 4303

    6. ELEE 4303 Shannon’s expansion theorem Any Boolean function f(w1, …, wn) can be written in the form Shannon’s expansion can be used multiple times Multiplexers can be used to implement any Boolean function based on Shannon’s expansion.

    7. ELEE 4303 Logic synthesis using multiplexers

    8. ELEE 4303

    9. ELEE 4303

    10. ELEE 4303 Lookup table (LUT) Commonly used logic elements in FPGA A 3-LUT can realize any logic function of three variables. A 4-variable function can be realized by three 3-LUTs through Shannon’s expension

    11. ELEE 4303 LUT synthesis

    12. ELEE 4303 Decoders Inputs: n-bit binary code Outputs: 2 -bit one-hot code (only one bit is asserted at a time) Each output corresponds to one valuation of the inputs.

    13. ELEE 4303 2-to-4 decoder

    14. ELEE 4303 4-to-16 decoder

    15. ELEE 4303 Application of decoder--ROM

    16. ELEE 4303 Encoders– opposite of decoder

    17. ELEE 4303 Priority encoders

    18. ELEE 4303 BCD-to-7-segment code

    19. ELEE 4303 Comparator

    20. ELEE 4303 Exercise Build a 8-to-1 multiplexer using 2-to-1 multiplexers and 4-to-1 multiplexers. Implement the function by 1) using a 3-to-8 binary decoder and an OR gate or 2) using a 2-to-1 multiplexer and any other necessary gates

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