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Decoders

Decoders. Usage of Decoders. Channel Selection: Generates Mutually Exclusive Channel Enabling/Disabling Signals (e.g. Multiplexers) Device Selection: Generates unique 1’s/0’s on output lines to turn on/off devices (e.g. decoder trees) Universal Function Implementation:

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Decoders

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  1. Decoders

  2. Usage of Decoders Channel Selection: Generates Mutually Exclusive Channel Enabling/Disabling Signals (e.g. Multiplexers) Device Selection: Generates unique 1’s/0’s on output lines to turn on/off devices (e.g. decoder trees) Universal Function Implementation: Serves as a device for implementing Boolean Functions on a Universal Basis Coding and Decoding Information: Can be used in a code/decode process (inputs can be recognized solely from outputs

  3. Functional Description and Symbols

  4. Where, N = {1, 2, 3, …..}

  5. Truth Table for a n-to-m Line Decoder

  6. Truth Table for a n-to-m Line Decoder

  7. Truth Table for a n-to-m Line Decoder (with enable)

  8. Truth Table for a n-to-m Line Decoder (with enable)

  9. Block-Symbolfor n-to-m Line Decoders Where, m = 2(n+1) – 1 n = {0,1, 2, 3, ….. , ∞}

  10. Truth Table for a 1-to-2 Line Decoder

  11. Block-Symbolfor 1-to-2 Line Decoders

  12. Truth Table for a 2-to-4 Line Decoder

  13. Block-Symbol for 2-to-4 Line Decoders

  14. Truth Table for a n-to-m Active-Low Line Decoder

  15. Truth Table for a n-to-m Line Active-Low Decoder (with enable)

  16. Block-Symbolfor n-to-m Line Active-Low Decoders Where, m = 2(n+1) – 1 n = {0,1, 2, 3, ….. , ∞}

  17. Decoder Trees

  18. A Larger Decoder using smaller Decoders 2-to-4 Line Decoder using 1-to-2 Line Decoders

  19. Device On/Off Truth Table

  20. Device On/Off Truth Table

  21. Device On/Off Truth Table

  22. A Decoder Tree operates on the principle of unique device selection by a Decoder i.e. the Decoders in the final level/stage are used for generating the unique outputs as required, while decoders in the previous stages are employed for device selection (in this case the devices are decoders in the final stage).

  23. Logical Truth Table of Decoder Tree

  24. Logical Truth Table of Decoder Tree

  25. Logical Truth Table of Decoder Tree

  26. Logical Truth Table of Decoder Tree

  27. Logical Truth Table of Decoder Tree

  28. Logical Truth Table of Decoder Tree

  29. Logical Truth Table of Decoder Tree

  30. Logical Truth Table of Decoder Tree

  31. 3-to-8 Line Decoder using 1-to-2 & 2-to-4 Line Decoders

  32. Boolean Function Realization

  33. Function Implementation Using Decoders

  34. Function Implementation Using Decoders

  35. Function Implementation Using Decoders

  36. Function Implementation Using Decoders

  37. Function Implementation Using Decoders f = m0 + m2 To implement the function we ‘OR’ the output pins d0 and d2 (which correspond to the Minterms m0 and m2). Using Relationships established using Duality f’ = m1 + m3 f = [ m1 + m3 ] ’ • F(x1, x2, …. , xn) = ∑mR = ∏MS • [F(x1, x2, …. , xn)]’ = ∑mS = ∏MR

  38. Function Implementation Using Decoders f = m0 + m2 f’ = m1 + m3 f = [ m1 + m3 ] ’

  39. Function Implementation Using Active-Low Decoders

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