Lecture11 Decoders

8/13/2019 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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Decoders!Typically ninputs and 2noutputs!Drives high the output corresponding to

binary code of input

74139


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2-to-4 Line Decoder

! Notice they are minterms


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Truth Table, 3-to-8 Decoder

!Notice they are minterms


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3-to-8 Line Decoder Schematic


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2-to-4 with Enable


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Enable Used for Expansion


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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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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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Uses for Decoders

!Implement logic circuits!!Memory address lines!Decoders are used in Micro

Computer Interfacing forKeyboard and Displayapplications.


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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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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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Encoder

! Encoder is the opposite of decoder! 2ninputs!

n outputs


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Truth Table


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Inputs are Minterms

A0= D1+ D3+ D5+ D7


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Whats the Problem?! What if D3 and D6 both high?! Simple OR circuit will set A to 7! Solution?


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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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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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Logic Diagram of a 4-input Priority

Encoder

X

Y

Lecture11 Decoders

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