Decoders
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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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Decoders

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Decoders

Decoders


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


Functional description and symbols

Functional Description and Symbols


Decoders

Where,

N = {1, 2, 3, …..}


Decoders

Truth Table for a n-to-m Line Decoder


Decoders

Truth Table for a n-to-m Line Decoder


Decoders

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


Decoders

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


Decoders

Block-Symbolfor n-to-m Line Decoders

Where,

m = 2(n+1) – 1

n = {0,1, 2, 3, ….. , ∞}


Decoders

Truth Table for a 1-to-2 Line Decoder


Decoders

Block-Symbolfor 1-to-2 Line Decoders


Decoders

Truth Table for a 2-to-4 Line Decoder


Decoders

Block-Symbol for 2-to-4 Line Decoders


Decoders

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


Decoders

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


Decoders

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

Where,

m = 2(n+1) – 1

n = {0,1, 2, 3, ….. , ∞}


Decoder trees

Decoder Trees


Decoders

A Larger Decoder using smaller Decoders

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


Decoders

Device On/Off Truth Table


Decoders

Device On/Off Truth Table


Decoders

Device On/Off Truth Table


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).


Decoders

Logical Truth Table of Decoder Tree


Decoders

Logical Truth Table of Decoder Tree


Decoders

Logical Truth Table of Decoder Tree


Decoders

Logical Truth Table of Decoder Tree


Decoders

Logical Truth Table of Decoder Tree


Decoders

Logical Truth Table of Decoder Tree


Decoders

Logical Truth Table of Decoder Tree


Decoders

Logical Truth Table of Decoder Tree


Decoders

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


Boolean function realization

Boolean Function Realization


Decoders

Function Implementation Using Decoders


Decoders

Function Implementation Using Decoders


Decoders

Function Implementation Using Decoders


Decoders

Function Implementation Using Decoders


Decoders

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


Decoders

Function Implementation Using Decoders

f = m0 + m2

f’ = m1 + m3

f = [ m1 + m3 ] ’


Decoders

Function Implementation Using Active-Low Decoders


Decoders

Function Implementation Using Active-Low Decoders


Decoders

Function Implementation Using Active-Low Decoders


Decoders

Function Implementation Using Active-Low Decoders


Decoders

Function Implementation Using Active-Low Decoders

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


Decoders

Function Implementation Using Active-Low Decoders

f = M1 . M3

f’ = M0 . M2

f = [ M0 . M2 ] ’


Decoders

Multiple Output Function Implementation Using Decoders


Decoders

Multiple Output Function Implementation Using Decoders


Decoders

Multiple Output Function Implementation Using Decoders


Decoders

Multiple Output Function Implementation Using Decoders


Decoders

Multiple Output Function Implementation Using Decoders


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