PLA Page 1 ECEn 224 PLAs Programmable Logic Arrays.
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PLA Page 1 ECEn 224 PLAs Programmable Logic Arrays
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Transcript of PLA Page 1 ECEn 224 PLAs Programmable Logic Arrays.
PLA Page 1
ECEn 224
PLAs
Programmable Logic Arrays
PLA Page 2
ECEn 224
PLAs Objectives
• Explain the operation of a PLA
• Use a PLA to implement a logic network
• Given a PLA design, determine the logic functions implemented
PLA Page 3
ECEn 224
Programmable Logic Array (PLA)
...
n Input Lines
ANDArray
...
m Outputs Lines
.
.
.OR
Array
k Word Lines
PLA Page 4
ECEn 224
PLA AND-OR Equivalent
F1 = AB’+ C
F2 = A’C’ + BC
F3 = AB’ + A’C’
F4 = A’C’ + BC + AB’C
ANDArray
ORArray
AB'
C
A'C'
BC
AB'C
CBA
F1
F2
F3
F4
Note: Not every minterm is available
PLA Page 5
ECEn 224
ProductI nput
(Actual)I nput
(Specified) OutputsTerm A A' B B' C C' A B C F1 F2 F3 F4
AB' 1 0 0 1 0 0 1 0 - 1 0 1 0C 0 0 0 0 1 0 - - 1 1 0 0 0
A'C' 0 1 0 0 0 1 0 - 0 0 1 1 1BC 0 0 1 0 1 0 - 1 1 0 1 0 1
AB'C 1 0 0 1 1 0 1 0 1 0 0 0 1
PLA Table Generation
F1 = AB’+ C
F2 = A’C’ + BC
F3 = AB’ + A’C’
F4 = A’C’ + BC + AB’C
PLA Page 6
ECEn 224
+ V
+ V + V
+ V
+ V
A B C
A' B' C'
F1
F2
F3
F4
AB'
CA'C'
BC
AB'C
Internal PLA Structure
Outputs
Inputs
+ V
+ V + V
+ V
+ V
A B C
A' B' C'
F1
F2
F3
F4
AB'
CA'C'
BC
AB'C
PLA Page 7
ECEn 224
Internal PLA Structure
Outputs
Inputs
The AND plane lines get pulled up to +V
PLA Page 8
ECEn 224
+ V
+ V + V
+ V
+ V
A B C
A' B' C'
F1
F2
F3
F4
AB'
CA'C'
BC
AB'C
Internal PLA Structure
The AND plane lines stay at +V unless oneof the connected inputs pulls it low.
0
Outputs
Inputs
PLA Page 9
ECEn 224
+ V
+ V + V
+ V
+ V
A B C
A' B' C'
F1
F2
F3
F4
AB'
CA'C'
BC
AB'C
Internal PLA Structure
The AND plane lines stay at +V unless oneof the connected inputs pulls it low.
1
Outputs
Inputs
PLA Page 10
ECEn 224
+ V
+ V + V
+ V
+ V
A B C
A' B' C'
F1
F2
F3
F4
AB'
CA'C'
BC
AB'C
Internal PLA Structure
The OR plane lines get pulled down to Ground
Outputs
Inputs
PLA Page 11
ECEn 224
+ V
+ V + V
+ V
+ V
A B C
A' B' C'
F1
F2
F3
F4
AB'
CA'C'
BC
AB'C
Internal PLA Structure
The OR plane lines get pulled down to Ground
Outputs
Inputs
PLA Page 12
ECEn 224
+ V
+ V + V
+ V
+ V
A B C
A' B' C'
F1
F2
F3
F4
AB'
CA'C'
BC
AB'C
Internal PLA Structure
The OR plane lines stay at GND unless oneof the AND plane lines pulls it high.
Outputs
Inputs
PLA Page 13
ECEn 224
+ V
+ V + V
+ V
+ V
A B C
A' B' C'
F1
F2
F3
F4
AB'
CA'C'
BC
AB'C
Internal PLA Structure
The OR plane lines stay at GND unless oneof the AND plane lines pulls it high.
Outputs
Inputs
PLA Page 14
ECEn 224
+ V
+ V + V
+ V
+ V
A B C
A' B' C'
F1
F2
F3
F4
AB'
CA'C'
BC
AB'C
Internal PLA Structure
The OR plane lines stay at GND unless oneof the AND plane lines pulls it high.
Outputs
Inputs
PLA Page 15
ECEn 224
+ V
+ V + V
+ V
+ V
A B C
A' B' C'
F1
F2
F3
F4
AB'
CA'C'
BC
AB'C
Internal PLA Structure
The OR plane lines stay at GND unless oneof the AND plane lines pulls it high.
Outputs
Inputs
PLA Page 16
ECEn 224
Another PLA Representation
Outputs
Inputs
AB'
C
A'C'
BC
AB'C
CBA
F1
F2
F3
F4
PLA Page 17
ECEn 224
Programmable Logic Array (PLA)
• All inputs and inverted inputs available• Limited number of AND functions
– This is the biggest difference between a ROM and a PLA
• Complete choice of inputs and inverted inputs for each AND function
• OR function for each output• Complete choice of AND functions for
each OR function (output)
PLA Page 18
ECEn 224
PLA Example
Implement these equations:X = ABC + B’D’ + AB’D + C’D’Y = BC + D’Z = CD + B’D’ + A’BC
in this PLA:CBA D
X Y Z
6 terms or ANDplane lines
8 terms
1 2 3 4
5 6
7 2 8
How can we implement 8 product terms with 6 AND plane lines?
PLA Page 19
ECEn 224
PLA Example
Implement these equations:X = ABC + B’D’ + AB’D + C’D’Y = BC + D’Z = CD + B’D’ + A’BC
A B X A B Y A B Z
C D 00 01 11 10 C D 00 01 11 10 C D 00 01 11 10
00 00 00
01 01 01
11 11 11
10 10 10
PLA Page 20
ECEn 224
PLA Example
Implement these equations:X = ABC + B’D’ + AB’D + C’D’Y = BC + D’Z = CD + B’D’ + A’BC
A B X A B Y A B Z
C D 00 01 11 10 C D 00 01 11 10 C D 00 01 11 10
00 1 1 1 1 00 00
01 1 01 01
11 1 1 11 11
10 1 1 1 10 10
PLA Page 21
ECEn 224
PLA Example
Implement these equations:X = ABC + B’D’ + AB’D + C’D’Y = BC + D’Z = CD + B’D’ + A’BC
A B X A B Y A B Z
C D 00 01 11 10 C D 00 01 11 10 C D 00 01 11 10
00 1 1 1 1 00 1 1 1 1 00
01 1 01 01
11 1 1 11 1 1 11
10 1 1 1 10 1 1 1 1 10
PLA Page 22
ECEn 224
PLA Example
Implement these equations:X = ABC + B’D’ + AB’D + C’D’Y = BC + D’Z = CD + B’D’ + A’BC
A B X A B Y A B Z
C D 00 01 11 10 C D 00 01 11 10 C D 00 01 11 10
00 1 1 1 1 00 1 1 1 1 00 1 1
01 1 01 01
11 1 1 11 1 1 11 1 1 1 1
10 1 1 1 10 1 1 1 1 10 1 1 1
A B X A B Y A B Z
C D 00 01 11 10 C D 00 01 11 10 C D 00 01 11 10
00 1 1 1 1 00 1 1 1 1 00 1 1
01 1 01 01
11 1 1 11 1 1 11 1 1 1 1
10 1 1 1 10 1 1 1 1 10 1 1 1
PLA Page 23
ECEn 224
PLA Example
C’D’ is in X and Y and looks useful
B’D’ is in all three functions
PLA Page 24
ECEn 224
PLA Example
C’D’ is in X and Y and looks useful
A B X A B Y A B Z
C D 00 01 11 10 C D 00 01 11 10 C D 00 01 11 10
00 1 1 1 1 00 1 1 1 1 00 1 1
01 1 01 01
11 1 1 11 1 1 11 1 1 1 1
10 1 1 1 10 1 1 1 1 10 1 1 1
PLA Page 25
ECEn 224
PLA Example
C’D’ is in X and Y and looks useful
B’D’ is in all three functions
A’BC and ABC cover a lot of minterms
A B X A B Y A B Z
C D 00 01 11 10 C D 00 01 11 10 C D 00 01 11 10
00 1 1 1 1 00 1 1 1 1 00 1 1
01 1 01 01
11 1 1 11 1 1 11 1 1 1 1
10 1 1 1 10 1 1 1 1 10 1 1 1
B’D’ is in all three functions
PLA Page 26
ECEn 224
PLA Example
C’D’ is in X and Y and looks useful
The only ones left are AB’ and CD
A’BC and ABC cover a lot of minterms
A B X A B Y A B Z
C D 00 01 11 10 C D 00 01 11 10 C D 00 01 11 10
00 1 1 1 1 00 1 1 1 1 00 1 1
01 1 01 01
11 1 1 11 1 1 11 1 1 1 1
10 1 1 1 10 1 1 1 1 10 1 1 1
PLA Page 27
ECEn 224
PLA Example
X = C’D’ + B’D’ + AB’ + ABCY = C’D’ + B’D’ + ABC + A’BCZ = B’D’ + CD + A’BC
A B X A B Y A B Z
C D 00 01 11 10 C D 00 01 11 10 C D 00 01 11 10
00 1 1 1 1 00 1 1 1 1 00 1 1
01 1 01 01
11 1 1 11 1 1 11 1 1 1 1
10 1 1 1 10 1 1 1 1 10 1 1 1
All of the functions are covered using only 6 product terms
How is this possible?
PLA Page 28
ECEn 224
PLA Example
X = C’D’ + B’D’ + AB’ + ABCY = C’D’ + B’D’ + ABC + A’BCZ = B’D’ + CD + A’BC
Product I nput OutputTerm A B C D X Y Z
C'D'B'D'AB'ABCA'BCCD
PLA Page 29
ECEn 224
PLA Example
X = C’D’ + B’D’ + AB’ + ABCY = C’D’ + B’D’ + ABC + A’BCZ = B’D’ + CD + A’BC
Product I nput OutputTerm A B C D X Y Z
C'D' - - 0 0B'D' - 0 - 0AB' 1 0 - -ABC 1 1 1 -A'BC 0 1 1 -CD - - 1 1
PLA Page 30
ECEn 224
PLA Example
X = C’D’ + B’D’ + AB’ + ABCY = C’D’ + B’D’ + ABC + A’BCZ = B’D’ + CD + A’BC
Product I nput OutputTerm A B C D X Y Z
C'D' - - 0 0 1 1 0B'D' - 0 - 0 1 1 1AB' 1 0 - - 1 0 0ABC 1 1 1 - 1 1 0A'BC 0 1 1 - 0 1 1CD - - 1 1 0 0 1
PLA Page 31
ECEn 224
PLA ExampleX = C’D’ + B’D’ + AB’ + ABC
Y = C’D’ + B’D’ + ABC + A’BC
Z = B’D’ + CD + A’BC
Product I nput OutputTerm A B C D X Y Z
C'D' - - 0 0 1 1 0B'D' - 0 - 0 1 1 1AB' 1 0 - - 1 0 0ABC 1 1 1 - 1 1 0A'BC 0 1 1 - 0 1 1CD - - 1 1 0 0 1
CBA D
X Y Z
PLA Page 32
ECEn 224
Summary
• Explain the operation of a ROM
• Use a ROM to implement a logic network
• Explain the operation of a PLA
• Use a PLA to implement a logic network
• Given a PLA design, determine the logic functions implemented
