Transcript [Decoders]

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
Universal Basis
a
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)
Block-Symbol for n-to-m Line Decoders
Where,
m = 2(n+1) – 1
n = {0,1, 2, 3, ….. , ∞}
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)
Block-Symbol for n-to-m Line Active-Low Decoders
Where,
m = 2(n+1) – 1
n = {0,1, 2, 3, ….. , ∞}
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
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
f = m0 + m2
f’ = m1 + m3
f = [ m1 + m3 ] ’
Function Implementation Using Active-Low Decoders
Function Implementation Using Active-Low Decoders
Function Implementation Using Active-Low Decoders
Function Implementation Using Active-Low 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
Function Implementation Using Active-Low Decoders
f = M1 . M3
f’ = M0 . M2
f = [ M0 . M2 ] ’
Multiple Output Function Implementation Using Decoders
Multiple Output Function Implementation Using Decoders
Multiple Output Function Implementation Using Decoders
Multiple Output Function Implementation Using Decoders
Multiple Output Function Implementation Using Decoders