Formula sheet: Encoders & Decoders | Digital Circuits - Electronics and Communication Engineering (ECE) PDF Download

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Enco ders & Deco ders F orm ula Sheet for GA TE
(Digital Circuits)
Enco ders
• Definition : Con v erts an activ e input signal in to a co ded output (e.g., binary or BCD).
• n-to-m Enco der : Con v erts 2
n
inputs to n binary outputs.
• 4-to-2 Enco der Example :
Y
1
=D
2
+D
3
, Y
0
=D
1
+D
3
where D
0
,D
1
,D
2
,D
3
are input lines, Y
1
,Y
0
are output bits.
• Priorit y Enco der : Assigns priorit y to inputs; outputs co de of highest-priorit y activ e
input.
Example (4-to-2 Priorit y Enco der):
Y
1
=D
3
+D
2
·D
3
, Y
0
=D
3
+D
1
·D
2
·D
3
, V =D
0
+D
1
+D
2
+D
3
where V is the v alid output indicator.
• 8-to-3 Enco der :
Y
2
=D
4
+D
5
+D
6
+D
7
, Y
1
=D
2
+D
3
+D
6
+D
7
, Y
0
=D
1
+D
3
+D
5
+D
7
Deco ders
• Definition : Con v erts n binary inputs in to 2
n
unique outputs.
• 2-to-4 Deco der Example :
D
0
=A
1
·A
0
, D
1
=A
1
·A
0
, D
2
=A
1
·A
0
, D
3
=A
1
·A
0
where A
1
,A
0
are input bits, D
0
to D
3
are output lines.
• 3-to-8 Deco der :
D
i
=A
b
2
2
·A
b
1
1
·A
b
0
0
where i is the decimal equiv alen t of binary input A
2
A
1
A
0
, and b
2
b
1
b
0
is the binary
represen tation of i .
• Enable Input : Man y deco ders ha v e an enable pin (E ); output is activ e only when
E =1 .
D
i
=A
b
2
2
·A
b
1
1
·A
b
0
0
·E
Applications
• Enco ders : Used in k eyb oards, data compression, and priorit y in terrupt systems.
• Deco ders : Used in memory addressing, dem ultiplexing, and displa y driv ers (e.g.,
7-segmen t displa y).
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Page 2


Enco ders & Deco ders F orm ula Sheet for GA TE
(Digital Circuits)
Enco ders
• Definition : Con v erts an activ e input signal in to a co ded output (e.g., binary or BCD).
• n-to-m Enco der : Con v erts 2
n
inputs to n binary outputs.
• 4-to-2 Enco der Example :
Y
1
=D
2
+D
3
, Y
0
=D
1
+D
3
where D
0
,D
1
,D
2
,D
3
are input lines, Y
1
,Y
0
are output bits.
• Priorit y Enco der : Assigns priorit y to inputs; outputs co de of highest-priorit y activ e
input.
Example (4-to-2 Priorit y Enco der):
Y
1
=D
3
+D
2
·D
3
, Y
0
=D
3
+D
1
·D
2
·D
3
, V =D
0
+D
1
+D
2
+D
3
where V is the v alid output indicator.
• 8-to-3 Enco der :
Y
2
=D
4
+D
5
+D
6
+D
7
, Y
1
=D
2
+D
3
+D
6
+D
7
, Y
0
=D
1
+D
3
+D
5
+D
7
Deco ders
• Definition : Con v erts n binary inputs in to 2
n
unique outputs.
• 2-to-4 Deco der Example :
D
0
=A
1
·A
0
, D
1
=A
1
·A
0
, D
2
=A
1
·A
0
, D
3
=A
1
·A
0
where A
1
,A
0
are input bits, D
0
to D
3
are output lines.
• 3-to-8 Deco der :
D
i
=A
b
2
2
·A
b
1
1
·A
b
0
0
where i is the decimal equiv alen t of binary input A
2
A
1
A
0
, and b
2
b
1
b
0
is the binary
represen tation of i .
• Enable Input : Man y deco ders ha v e an enable pin (E ); output is activ e only when
E =1 .
D
i
=A
b
2
2
·A
b
1
1
·A
b
0
0
·E
Applications
• Enco ders : Used in k eyb oards, data compression, and priorit y in terrupt systems.
• Deco ders : Used in memory addressing, dem ultiplexing, and displa y driv ers (e.g.,
7-segmen t displa y).
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Example: 2-to-4 Deco der T ruth T able
A
1
A
0
D
0
D
1
D
2
D
3
0 0 1 0 0 0
0 1 0 1 0 0
1 0 0 0 1 0
1 1 0 0 0 1
Key Notes
• Enco ders assume only one input is activ e unless sp ecified as priorit y enco ders.
• Deco ders pro duce min terms; eac h output corresp onds to a unique input com bination.
• F or GA TE, fo cus on Bo olean expressions and priorit y enco der logic.
• Use K-maps to simplify enco der/deco der logic if needed.
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