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
Truth Table for a n-to-m Line Decoder (with enable)
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
Device On/Off Truth Table
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
Logical Truth Table of Decoder Tree
Logical Truth Table of Decoder Tree
Logical Truth Table of Decoder Tree
Logical Truth Table of Decoder Tree
Logical Truth Table of Decoder Tree
Logical Truth Table of Decoder Tree
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
Function Implementation Using Decoders
Function Implementation Using Decoders
Function Implementation Using Decoders
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 ] ’