lecture11 decoders
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14/11/2013
Combinational Logic Design
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Fall 2013 EC381/Digital Systems I 2
Topics
! Decoders! Encoders! Priority Encoders
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Fall 2013 EC381/Digital Systems I 3
Decoders!Typically ninputs and 2noutputs!Drives high the output corresponding to
binary code of input
74139
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Fall 2013 EC381/Digital Systems I 4
2-to-4 Line Decoder
! Notice they are minterms
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Fall 2013 EC381/Digital Systems I 5
Truth Table, 3-to-8 Decoder
!Notice they are minterms
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Fall 2013 EC381/Digital Systems I 6
3-to-8 Line Decoder Schematic
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Fall 2013 EC381/Digital Systems I 7
2-to-4 with Enable
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Fall 2013 EC381/Digital Systems I 8
Enable Used for Expansion
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Fall 2013 EC381/Digital Systems I 9
VariationsSometimes, in implementation decoders are done with NANDgates rather than AND gates.With NAND gates, the table illustrating the decoder
operation would look like this:
So pay attention In using a decoder, it is useful to know
when the output is intended to be active high, or activelow!
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Fall 2013 EC381/Digital Systems I 10
Decoder Expansion
! A 2-to-4 Line decoder requires 4 (2-input)AND gates! A 3-to-8 line decoder requires 8(3-input)AND gates! If we want to design a 6-to-64 line decoder then we
will need?
! 64(6-input)AND gates!! Unfortunately, as decoders become larger, this
approach gives a high gate input count!
! If we have decoders with enables, we can usemultiple, small decoders to implement largerdecoders.
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Decoder Expansion: Example
!4to16 decoder Using 3to8decoders
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Decoder Expansion Example! When w =0, the
topdecoder isenabled and the
other is disabled.! The bottom
decoder outputsare all 0s, andthe top eightoutputs generate
minterms! 0000 to 0111.
When w =1, theenable conditionsare reversed
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Example decoder tree: 4to16
decoder Using 2
to
4 decoders
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Fall 2013 EC381/Digital Systems I 14
Uses for Decoders
!Implement logic circuits!!Memory address lines!Decoders are used in Micro
Computer Interfacing forKeyboard and Displayapplications.
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Fall 2013 EC381/Digital Systems I 15
Decoder generates appropriateminterm based on control signals
(it "decodes" control signals)
Decoders as General-purpose Logic
! n:2ndecoder implements any function of n variables" With the variables used as control inputs" Enable inputs tied to 1 and" Appropriate minterms summed to form the function
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Decoders as General-purpose
Logic! Example: Implement the following boolean functions
1. S(x,y,z) = SUM(m(1,2,4,7))2. C(x,y,z) = SUM(m(3,5,6,7))
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Fall 2013 EC381/Digital Systems I 17
F1
Example
! F1 = A' B C' D + A' B' C D + A B C D
A B
0 A'B'C'D'
1 A'B'C'D
2 A'B'CD'
3 A'B'CD4 A'BC'D'
5 A'BC'D
6 A'BCD'
7 A'BCD
8 AB'C'D'
9 AB'C'D
10 AB'CD'
11 AB'CD
12 ABC'D'
13 ABC'D
14 ABCD'
15 ABCD
4:16
DECEnable
C D
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Fall 2013 EC381/Digital Systems I 18
Encoder
! Encoder is the opposite of decoder! 2ninputs!
n outputs
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Fall 2013 EC381/Digital Systems I 19
Truth Table
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Fall 2013 EC381/Digital Systems I 20
Inputs are Minterms
A0= D1+ D3+ D5+ D7
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Fall 2013 EC381/Digital Systems I 21
Whats the Problem?! What if D3 and D6 both high?! Simple OR circuit will set A to 7! Solution?
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Fall 2013 EC381/Digital Systems I 22
Priority Encoder! Chooses one with highest priority
" Largest number, usually! Note dont cares
What if all inputs are zero?
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Priority Encoder
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Fall 2013 EC381/Digital Systems I 24
K Map for a priority encoder
!X on input means we must satisfy forboth possibilities: 0, 1
Valid (V) is OR
of inputs
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K Map for a priority encoder
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Fall 2013 EC381/Digital Systems I 26
Logic Diagram of a 4-input Priority
Encoder
X
Y
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