Implementation of Boolean Functions using PLA
Introduction to PLA
A Programmable Logic Array (PLA) is a hardware device used to implement combinational logic circuits. It consists of a programmable AND array and a programmable OR array, allowing for customizable logic functions.
Function Definitions
- F1(A,B,C) = Σ(0,1,3,5)
- F2(A,B,C) = Π(0,3,5,7)
Minimization of Functions
To implement these functions, we first need to derive their truth tables and simplified forms.
- F1 Truth Table:
- Outputs 1 for minterms 0, 1, 3, and 5.
- Corresponding binary inputs:
- 000 -> 1
- 001 -> 1
- 011 -> 1
- 101 -> 1
- F2 Complement Truth Table:
- Outputs 0 for maxterms 0, 3, 5, and 7.
- Outputs 1 for minterms 1, 2, 4, 6.
Programming the AND Array
The AND array will contain the necessary product terms for both functions:
- For F1:
- P1 = A'B'C'
- P2 = A'B'C
- P3 = A'BC
- P4 = AB'C
- For F2:
- P1 = A'B'C'
- P2 = A'BC'
- P3 = AB'C
Programming the OR Array
Next, we connect the outputs of the AND array to the OR array:
- For F1: Connect outputs of P1, P2, P3, and P4 to an OR gate.
- For F2: Connect outputs of only P1 and P2 (complemented).
Conclusion
By configuring the AND and OR arrays according to these product terms, the PLA can effectively implement the desired Boolean functions F1 and F2. This method allows for efficient combinational logic design in electronic circuits.