1. Programmable Logic Arrays, Test Review
Today:
First Hour: Programmable Logic Arrays
Section 4.1 of Katz’s Textbook
In-class Activity #1
Second Hour:Test #1 Q&A, Review.

2. Recap: Simplifying Larger Functions
Use Logic Minimization software.
Example: espresso
Public domain, Easy to use, yet Serious enough for the real world.
.i 3
.o 3
.p 8 .e
a2 a1 a0 b2 b1 b0
x x x
x x x
x x x
.i 3
.o 3
.p 4 .e
b2 = a1 a0
b1 = a1' a0 + a1 a0'
b0 = a2' a0'

3. Implementing Larger Circuits: Programmable Logic Arrays
Old technology:
Buy chips with gates (e.g., a chip with 4 NAND gates), and wire them up to build logic circuits
messy wiring,
error prone
takes lots of space and power
Newer technology:
Buy a single programmable logic array (PLA) chip
Customize this chip to implement our function
Can be as easy as downloading an espresso output to a “PLA programmer.”

4. PLA Example
Need to implement the following 3-input, 4-output function:
F0 = A + B' C'
F1 = A C' + A B
F2 = B' C' + A B
F3 = B' C + A

5. Blank PLA
A B C
F F F F3

6. After Programming Note: F1 and F2 reuse AB 1 A B C A B B' C A C' B' C'
F0 = A + B' C'
F1 = A C' + A B
F2 = B' C' + A B
F3 = B' C + A
F F F F3

7. Key to Efficiency: Reuse Shared Terms
F0 = A + B' C'
F1 = A C' + A B
F2 = B' C' + A B
F3 = B' C + A
B' C' A
A B

8. “Personality Matrix” Product t erm Inputs Outputs F 1 F F 1 F 1 A 1 -1 F 1 F 2 1 F 3 1 A 1 - B 1 - C - 1
A B
Reuse of
terms
B' C
A C'
B' C' A

9. How Programming Works Fuse on each gate input
Blow the fuse with a large current - disconnect that input
Use SW to do this.
(Blowing the wrong fuse would be annoying.)
Other technologies are also used in PLAs, besides fuses.

10. Everything is connected
Compact Form - Before
Everything is connected

11. Only desired connections remain
Compact Form - After
A B C D
A B
C D
Only desired connections remain
A B + A B
C D + C D

12. Programmable array logic
PAL
Programmable array logic
Minor variant on the PLA.
Each output function is OR of a fixed number of terms, say 4.
Does not exploit shared product terms.
E.g., 16x48x8 PAL:
16 inputs (and their complements).
48 terms ANDing those inputs (or complements)
(Note: 48 << 216).
8 output functions ORing those terms
If these restrictions are OK, then the PAL may be cheaper.

13. Simple PAL

14. Ex: BCD to Gray Code Non- standard Gray Code sequence A 1 B C D W X Y1 B C D W X Y Z
Non-
standard
Gray Code
sequence

15. K- maps K-map for W K-map for X K-map for Y K-map for Z AB AB CD 00 0111 10 CD 00 01 11 10 00 X 1 00 1 X 01 1 X 1 01 1 X 11 1 X X 11 X X 10 1 X X 10 X X
K-map for W
K-map for X AB AB CD 00 01 11 10 CD 00 01 11 10 00 1 X 00 X 1 01 1 X 01 1 X 11 1 1 X X 11 1 X X 10 1 1 X X 10 1 X X
K-map for Y
K-map for Z

16. Minimized Functions W = A + B D + B C X = B C' Y = B + C
Z = A' B' C' D + B C D + A D' + B' C D’
No shared terms

17. A B C D
PAL Implementation A
B D
B C B C
A B C D
B C D
A D
W X Y Z

18. Do Activity #1 Now For Next Class: Due: End of Class Today
RETAIN THE LAST PAGE (#3)!!
For Next Class:
Bring Randy Katz Textbook
Required Reading:
Sec 4.1, 4.2 of Katz
This reading is necessary for getting points in the Studio Activity!