decoders. outline useful msi circuits decoders implementing functions with decoders decoders...
TRANSCRIPT
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Decoders
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Outline
Useful MSI circuits
Decoders
Implementing Functions with Decoders
Decoders with Enable
Larger Decoders
Standard MSI Decoders
Implementing Functions with Decoders
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Outline
Useful MSI circuits
Decoders
Implementing Functions with Decoders
Decoders with Enable
Larger Decoders
Standard MSI Decoders
Implementing Functions with Decoders
![Page 4: Decoders. Outline Useful MSI circuits Decoders Implementing Functions with Decoders Decoders with Enable Larger Decoders Standard MSI Decoders](https://reader035.vdocuments.site/reader035/viewer/2022081503/56649dd45503460f94acb701/html5/thumbnails/4.jpg)
Useful MSI circuits
Four common and useful MSI circuits are: Decoder Encoder Demultiplexer Multiplexer
Block-level outlines of MSI circuits:
decodercode entity
encodercodeentity
mux datainput
select
demuxdata output
select
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Outline
Useful MSI circuits
Decoders
Implementing Functions with Decoders
Decoders with Enable
Larger Decoders
Standard MSI Decoders
Implementing Functions with Decoders
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Decoders (1/5)
Codes are frequently used to represent entities, e.g. your name is a code to denote yourself (an entity!).
These codes can be identified (or decoded) using a decoder. Given a code, identify the entity.
Convert binary information from n input lines to (max. of) 2n output lines.
Known as n-to-m-line decoder, or simply n:m or nm decoder (m 2n).
May be used to generate 2n (or fewer) minterms of n input variables.
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Decoders (2/5)
Example: if codes 00, 01, 10, 11 are used to identify four light bulbs, we may use a 2-bit decoder:
2x4Dec2-bit
codeX
Y
F0
F1
F2
F3
Bulb 0Bulb 1Bulb 2Bulb 3
This is a 24 decoder which selects an output line based on the 2-bit code supplied.
Truth table:X Y F0 F1 F2 F3
0 0 1 0 0 00 1 0 1 0 01 0 0 0 1 01 1 0 0 0 1
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Decoders (3/5)
From truth table, circuit for 24 decoder is:
Note:
Each output is a 2-variable minterm (X'.Y', X'.Y, X.Y' or X.Y)
X Y F0 F1 F2 F3
0 0 1 0 0 00 1 0 1 0 01 0 0 0 1 01 1 0 0 0 1
F0 = X'.Y'
F1 = X'.Y
F2 = X.Y'
F3 = X.Y
X Y
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Decoders (4/5)
Design a 38 decoder.
x y z F0 F1 F2 F3 F4 F5 F6 F7
0 0 0 1 0 0 0 0 0 0 00 0 1 0 1 0 0 0 0 0 00 1 0 0 0 1 0 0 0 0 00 1 1 0 0 0 1 0 0 0 01 0 0 0 0 0 0 1 0 0 01 0 1 0 0 0 0 0 1 0 01 1 0 0 0 0 0 0 0 1 01 1 1 0 0 0 0 0 0 0 1
F1 = x'.y'.z
x zy
F0 = x'.y'.z'
F2 = x'.y.z'
F3 = x'.y.z
F5 = x.y'.z
F4 = x.y'.z'
F6 = x.y.z'
F7 = x.y.z
Application?
Binary-to-octal conversion.
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Decoders (5/5)
In general, for an n-bit code, a decoder could select up to 2n lines:
: :n-bitcode
n to 2n
decoderup to 2n
output lines
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Outline
Useful MSI circuits
Decoders
Implementing Functions with Decoders
Decoders with Enable
Larger Decoders
Standard MSI Decoders
Implementing Functions with Decoders
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Decoders: Implementing Functions (1/5)
A Boolean function, in sum-of-minterms form decoder to generate the minterms, and an OR gate to form the sum.
Any combinational circuit with n inputs and m outputs can be implemented with an n:2n decoder with m OR gates.
Good when circuit has many outputs, and each function is expressed with few minterms.
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Decoders: Implementing Functions (2/5)
Example: Full adder
S(x, y, z) = m(1,2,4,7)
C(x, y, z) = m(3,5,6,7)
3x8Dec
S2
S1
S0
x
y
z
0
1
2
3
4
5
6
7
S
C
x y z C S0 0 0 0 00 0 1 0 10 1 0 0 10 1 1 1 01 0 0 0 11 0 1 1 01 1 0 1 01 1 1 1 1
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Decoders: Implementing Functions (3/5)
3x8Dec
S2
S1
S0
x
y
z
0
1
2
3
4
5
6
7
S
C
x y z C S0 0 0 0 00 0 1 0 10 1 0 0 10 1 1 1 01 0 0 0 11 0 1 1 01 1 0 1 01 1 1 1 1
10000000
0
0
0
0
0
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Decoders: Implementing Functions (4/5)
3x8Dec
S2
S1
S0
x
y
z
0
1
2
3
4
5
6
7
S
C
x y z C S0 0 0 0 00 0 1 0 10 1 0 0 10 1 1 1 01 0 0 0 11 0 1 1 01 1 0 1 01 1 1 1 1
01000000
1
0
0
0
1
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Decoders: Implementing Functions (5/5)
3x8Dec
S2
S1
S0
x
y
z
0
1
2
3
4
5
6
7
S
C
x y z C S0 0 0 0 00 0 1 0 10 1 0 0 10 1 1 1 01 0 0 0 11 0 1 1 01 1 0 1 01 1 1 1 1
00000001
1
1
1
1
1
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Outline
Useful MSI circuits
Decoders
Implementing Functions with Decoders
Decoders with Enable
Larger Decoders
Standard MSI Decoders
Implementing Functions with Decoders
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Decoders with Enable (1/2)
Decoders often come with an enable signal, so that the device is only activated when the enable, E=1.
Truth table:
E X Y F0 F1 F2 F3
1 0 0 1 0 0 01 0 1 0 1 0 01 1 0 0 0 1 01 1 1 0 0 0 10 X X 0 0 0 0
F0 = EX'Y'
F1 = EX'Y
F2 = EXY'
F3 = EXY
X Y E
Circuit:
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Decoders with Enable (2/2)
In the previous slide, the decoder has a one-enable signal, that is, the decoder is enabled with E=1.
In most MSI decoders, enable signal is zero-enable, usually denoted by E’ (or E). The decoder is enabled when the signal is zero.
E X Y F0 F1 F2 F3
1 0 0 1 0 0 01 0 1 0 1 0 01 1 0 0 0 1 01 1 1 0 0 0 10 X X 0 0 0 0
E' X Y F0 F1 F2 F3
0 0 0 1 0 0 00 0 1 0 1 0 00 1 0 0 0 1 00 1 1 0 0 0 11 X X 0 0 0 0
Decoder with 1-enable Decoder with 0-enable
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Outline
Useful MSI circuits
Decoders
Implementing Functions with Decoders
Decoders with Enable
Larger Decoders
Standard MSI Decoders
Implementing Functions with Decoders
![Page 21: Decoders. Outline Useful MSI circuits Decoders Implementing Functions with Decoders Decoders with Enable Larger Decoders Standard MSI Decoders](https://reader035.vdocuments.site/reader035/viewer/2022081503/56649dd45503460f94acb701/html5/thumbnails/21.jpg)
Larger Decoders (1/6)
Larger decoders can be constructed from smaller ones.
For example, a 3-to-8 decoder can be constructed from two 2-to-4 decoders (with one-enable), as follows:
3x8Dec
S2
S1
S0
wxy
01::7
F0 = w'x'y'F1 = w'x'y::F7 = wxy
2x4Dec
S1
S0
0123
F0 = w'x'y'F1 = w'x'yF2 = w'xy'F3 = w'xyE
2x4Dec
S1
S0
0123
F4 = wx'y'F5 = wx'yF6 = wxy'F7 = wxyE
wxy
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Larger Decoders (2/6)
3x8Dec
S2
S1
S0
wxy
01::7
F0 = w'x'y'F1 = w'x'y::F7 = wxy
2x4Dec
S1
S0
0123
F0 = w'x'y'F1 = w'x'yF2 = w'xy'F3 = w'xyE
2x4Dec
S1
S0
0123
F4 = wx'y'F5 = wx'yF6 = wxy'F7 = wxyE
wxy
000
0000
1000
0 = disabled
1 = enabled
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Larger Decoders (3/6)
3x8Dec
S2
S1
S0
wxy
01::7
F0 = w'x'y'F1 = w'x'y::F7 = wxy
2x4Dec
S1
S0
0123
F0 = w'x'y'F1 = w'x'yF2 = w'xy'F3 = w'xyE
2x4Dec
S1
S0
0123
F4 = wx'y'F5 = wx'yF6 = wxy'F7 = wxyE
wxy
001
0000
0100
0 = disabled
1 = enabled
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Larger Decoders (4/6)
3x8Dec
S2
S1
S0
wxy
01::7
F0 = w'x'y'F1 = w'x'y::F7 = wxy
2x4Dec
S1
S0
0123
F0 = w'x'y'F1 = w'x'yF2 = w'xy'F3 = w'xyE
2x4Dec
S1
S0
0123
F4 = wx'y'F5 = wx'yF6 = wxy'F7 = wxyE
wxy
110
0010
0000
1 = enabled
0 = disabled
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Larger Decoders (5/6)
Construct a 4x16 decoder from two 3x8 decoders with 1-enable.
4x16DecS3
S2
S1
S0
wxyz
01::
15
F0
F1
::F15
3x8Dec
S2
S1
S0
01:7
F0
F1
:F7E
3x8Dec
S2
S1
S0
01:7
F8
F9
:F15E
wxyz
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Larger Decoders (6/6)
Note: The input, w and its complement, w', is used to select either one of the two smaller decoders.
Decoders may also have zero-enable and/or negated outputs. (Normal outputs = active high; negated outputs = active low.)
Exercise:
What modifications must be made to provide an ENABLE input for the 3x8 decoder (2 slides ago) and the 4x16 decoder (previous slide) created?
Exercise:
How to construct a 4x16 decoder using five 2x4 decoders with enable?
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Outline
Useful MSI circuits
Decoders
Implementing Functions with Decoders
Decoders with Enable
Larger Decoders
Standard MSI Decoders
Implementing Functions with Decoders
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Standard MSI Decoders (1/2)
74138 (3-to-8 decoder)
74138 decoder module. (a) Logic circuit. (b) Package pin configuration.
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Standard MSI Decoders (2/2)
74138 decoder module.
(c) Function table.
74138 decoder module. (d) Generic symbol. (e) IEEE standard logic symbol.
Source: The Data Book Volume 2, Texas Instruments Inc.,1985
Negated outputs
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Outline
Useful MSI circuits
Decoders
Implementing Functions with Decoders
Decoders with Enable
Larger Decoders
Standard MSI Decoders
Implementing Functions with Decoders
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Decoders: Implementing Functions Revisit (1/2)
Example: Implement the following logic function using decoders and logic gates
f(Q,X,P) = m(0,1,4,6,7) = M(2,3,5)
We may implement the function in several ways:
(a) Use a decoder (with active-high outputs) with an OR gate:f(Q,X,P) = m0 + m1 + m4 + m6 + m7
(b) Use a decoder (with active-low outputs) with a NAND gate:
f(Q,X,P) = ( m0' . m1' . m4' . m6' . m7' )'
(c) Use a decoder (with active-high outputs) with a NOR gate:f(Q,X,P) = ( m2 + m3 + m5 )' [ = M2.M3.M5]
(d) Use a decoder (with active-low outputs) with an AND gate:f(Q,X,P) = m2' . m3' . m5'
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Decoders: Implementing Functions Revisit (2/2)
3x8Dec
A
B
C
Q
X
P
01234567
f(Q,X,P) f(Q,X,P)
3x8Dec
A
B
C
Q
X
P
01234567
3x8Dec
A
B
C
Q
X
P
01234567
f(Q,X,P) f(Q,X,P)
3x8Dec
A
B
C
Q
X
P
01234567
(a) Active-high decoder with OR gate. (b) Active-low decoder with NAND gate.
(c) Active-high decoder with NOR gate. (d) Active-low decoder with AND gate.
f(Q,X,P) = m(0,1,4,6,7)