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

Where, N = {1, 2, 3, …..}

Truth Table for a n-to-m Line Decoder

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

Where,m = 2(n+1) – 1n = {0,1, 2, 3, ….. , ∞}

Block-Symbol for n-to-m Line Decoders

Truth Table for a 1-to-2 Line Decoder

Block-Symbol for 1-to-2 Line Decoders

Truth Table for a 2-to-4 Line Decoder

Block-Symbol for 2-to-4 Line Decoders

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

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

Where,m = 2(n+1) – 1n = {0,1, 2, 3, ….. , ∞}

Block-Symbol for n-to-m Line Active-Low Decoders

Decoder Trees

A Larger Decoder using smaller Decoders

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

Device On/Off Truth Table

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

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

Boolean Function Realization

Function Implementation Using Decoders


To implement the function we ‘OR’ the output pins d0 and d2 (which correspond to the Minterms m0 and m2).

Using Relationships established using Dualityf’ = m1 + m3f = [ m1 + m3 ] ’

f = m0 + m2

F(x1, x2, …. , xn) = ∑mR = ∏MS [F(x1, x2, …. , xn)]’ = ∑mS = ∏MR


f’ = m1 + m3 f = [ m1 + m3 ] ’

f = m0 + m2

Function Implementation Using Active-Low Decoders


To implement the function we ‘OR’ the output pins d0 and d2 (which correspond to the Minterms m0 and m2).

Using Relationships established using Dualityf’ = M0 . M2 f = [ M0 . M2 ] ’

f = M1 . M3

F(x1, x2, …. , xn) = ∑mR = ∏MS [F(x1, x2, …. , xn)]’ = ∑mS = ∏MR


f’ = M0 . M2 f = [ M0 . M2 ] ’

f = M1 . M3

Multiple Output Function Implementation Using Decoders

Decoders

Documents

Transcript of Decoders