Combinational Circuits with Programmable Logic Devices

1
Combinational Circuits with Programmable Logic
Devices

• Programmable Logic Arrays (PLA)
• Programmable Read-Only Memory
• (PROM)

2
Programmable Logic Devices

• Any Boolean function can be expressed in a Sum of
  Product form
• SOP form gt AND-OR implementation
• Programmable Logic Devices
• Pre-fabricated building blocks of many AND/OR
  gates (or NOR, NAND)
• Programmed by making or breaking connections
  among the gates

3
Programmable Logic Devices
Block Diagram of a Programmable Array of AND and
OR for Sum of Products Form
Inputs
Array of OR gates
Outputs
4
Programmable Logic Devices

• Programmable Logic Array (PLA) The AND array and
  the OR array are programmable.
• Programmable Array Logic (PAL) The AND array is
  programmable but the OR array is fixed
• Programmable Read-Only Memory(PROM) The AND
  array is fixed and the OR array is programmable.

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PLA 3 inputs x 4 outputs
Inputs
All possible connections are available before
programming
Programmable OR array
Programmable AND Array
Outputs
6
PLAs

• Metal fuses are used by the manufacturer to
  establish the connections among the gates (i.e.
  between the inputs and the AND gates, and the AND
  gates and the OR gates).
• The metal fuses can be selectively removed
  (blown)
• A blown fuse behaves as an open circuit (i.e.
  no connection)
• An intact fuse behaves as a short circuit.
• Programming a PLA blowing fuses for unwanted
  connections.

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PLAs Alternative Diagram
Shorthand notation so we dont have to draw all
the wires!
Note The number of AND gates varies
8
PLAs Example

• F0 A B' C'
• F1 A C' A B
• F2 B' C' A B
• F3 B' C A

Key to Success Shared Product Terms
9
Example Continued
A B C
Unwanted connections are blown
F0 A B' C' F1 A C' A B F2 B' C'
A B F3 B' C A
AB
BC
AC
BC
A
Note of AND gates of product terms
F0 F1 F2 F3
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Example Continued
Fuse intact
A B C
AB
BC
AC
BC
F0 A B' C' F1 A C' A B F2 B' C'
A B F3 B' C A
A
F0 F1 F2 F3
11
0
Non-complement
1
Complement
12
Programming A PLA

• A PLA program table is needed to program a PLA
• A PLA may be Mask Programmable or Field
  Programmable
• Mask Programmable PLA customer/designer submits
  a PLA program table to manufacturer.
• Manufacturer produces a custom made PLA
• Field Programmable PLA PLA can be programmed by
  the user/designer using special instruments
  (device programmers)
• The size of a PLA is determined by three factors
• of inputs, of product terms, of outputs

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Design with PLA

• Given a function or a group of functions
• 1. Minimize function(s) using any method (K-map,
  McCluskey, etc). gt minimal SOP form.
• Minimize the number of product terms
• Number of literals is not important.
• Check each function and its complement.
• 2. If multiple functions, look for common product
  terms.
• 3. Derive PLA table
• 4. Draw PLA diagram
• of AND gates of distinct product terms
• of OR gates of outputs.
• Draw a X for each connection

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Design with PLA

• F1 ? m(0, 1, 5, 6, 7)
• F2 ? m(2, 3, 4, 7)
• Realize the above two functions using the
  smallest PLA.

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8 x 4 PROM
Fuse Fixed Connection
m1
m2
Programmable OR Array
m3
m4
m5
m6
m7
Fixed AND Array Generates All Minterms
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8 x 4 PROM
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Programmable ROM

• 1. 2N x M PROM N inputs and M outputs
• gt can implement M Boolean functions of N
  variables.
• 2. PROM implements the sum of minterms form of
  functions gt no need to minimize
• gt easier to design with PROM than PLA

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Boolean Functions with PROM

• Realize the following three functions using a
  3-input, 3-output PROM
• F1(A, B, C) AB B'C
• F2(A, B, C) (AB'C).(A'B)
• F3(A, B, C) A BC
• Step1 Put expressions in standard SOP form
• F1(A, B, C) ? m ( 1, 5, 6, 7)
• F2(A, B, C) ? m ( 0, 1, 3, 6, 7)
• F3(A, B, C) ? m ( 3, 4, 5, 6, 7)
• Step2 Draw PROM diagram

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Boolean Functions with PROM
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Programmable ROM

• Conceptually, an 2N x M PROM can be viewed as a
  memory device
• capacity of 2N words
• each word is M bits wide
• The N inputs represent the address of the memory
  location to access in the PROM
• The N bit address is decoded using an N to 2N
  decoder.
• The decoder activates one memory location which
  is read.

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PROM as a Storage Device

• Store the following data in a PROM of appropriate
  size in the sequence indicated
• 0001 10
• 1010 01
• 1101 10
• 0110 01
• 0101 01
• 1110 01
• 1001 11
• 0110 10