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

6. Where, N = {1, 2, 3, …..}

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

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

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

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

13. Block-Symbol for 1-to-2 Line Decoders

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

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

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

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

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

19. Decoder Trees

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

21. Device On/Off Truth Table

24. 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).

25. Logical Truth Table of Decoder Tree

34. 3-to-8 Line Decoder using 1-to-2 & 2-to-4 Line Decoders

43. Boolean Function Realization

44. Function Implementation Using Decoders

48. To implement the function we ‘OR’ the output pins d 0 and d 2 (which correspond to the Minterms m0 and m2). Using Relationships established using Duality f’ = m1 + m3 f = [ m1 + m3 ] ’ f = m0 + m2 F(x1, x2, …., xn) = ∑m R = ∏M S [F(x1, x2, …., xn)]’ = ∑m S = ∏M R

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

50. Function Implementation Using Active-Low Decoders

54. To implement the function we ‘OR’ the output pins d 0 and d 2 (which correspond to the Minterms m0 and m2). Using Relationships established using Duality f’ = M0. M2 f = [ M0. M2 ] ’ f = M1. M3 F(x1, x2, …., xn) = ∑m R = ∏M S [F(x1, x2, …., xn)]’ = ∑m S = ∏M R

55. Function Implementation Using Active-Low Decoders f’ = M0. M2 f = [ M0. M2 ] ’ f = M1. M3

56. Multiple Output Function Implementation Using Decoders