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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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Usage of 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:

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



Where,

N = {1, 2, 3, …..}






Block-Symbolfor n-to-m Line Decoders

Where,

m = 2(n+1) – 1

n = {0,1, 2, 3, ….. , ∞}



Block-Symbolfor 1-to-2 Line Decoders



Block-Symbol for 2-to-4 Line Decoders



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


Block-Symbolfor n-to-m Line Active-Low Decoders

Where,

m = 2(n+1) – 1

n = {0,1, 2, 3, ….. , ∞}



A Larger Decoder using smaller Decoders

2-to-4 Line Decoder using 1-to-2 Line Decoders





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).


Logical Truth Table of Decoder Tree 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).


Logical Truth Table of Decoder Tree 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).


Logical Truth Table of Decoder Tree 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).


Logical Truth Table of Decoder Tree 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).


Logical Truth Table of Decoder Tree 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).


Logical Truth Table of Decoder Tree 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).


Logical Truth Table of Decoder Tree 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).


Logical Truth Table of Decoder Tree 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).


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


Boolean function realization

Boolean Function Realization 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).


Function Implementation Using Decoders 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).


Function Implementation Using Decoders 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).


Function Implementation Using Decoders 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).


Function Implementation Using Decoders 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).


Function Implementation Using Decoders 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).

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


Function Implementation Using Decoders 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).

f = m0 + m2

f’ = m1 + m3

f = [ m1 + m3 ] ’


Function Implementation Using Active-Low Decoders 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).


Function Implementation Using Active-Low Decoders 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).


Function Implementation Using Active-Low Decoders 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).


Function Implementation Using Active-Low Decoders 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).


Function Implementation Using Active-Low Decoders 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).

f = M1 . M3

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’ = M0 . M2

f = [ M0 . M2 ] ’

  • F(x1, x2, …. , xn) = ∑mR = ∏MS

  • [F(x1, x2, …. , xn)]’ = ∑mS = ∏MR


Function Implementation Using Active-Low Decoders 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).

f = M1 . M3

f’ = M0 . M2

f = [ M0 . M2 ] ’


Multiple Output Function Implementation Using Decoders 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).


Multiple Output Function Implementation Using Decoders 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).


Multiple Output Function Implementation Using Decoders 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).


Multiple Output Function Implementation Using Decoders 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).


Multiple Output Function Implementation Using Decoders 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).


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