Question

Problem 13: A(X,Y,Z) = ∑(2,3,4,5,6) B(X,Y,Z) = X’y’z’ + Xy’ + X’yz’ C(X,Y,Z) = Xy’z’ + X’y + Xyz’ A. Tabulate The Truth Table For A ROM That Implements The 3 Boolean Functions A,B,C. Draw The Circuit. Specify The Size Of The ROM. B. Draw The PLA Circuit That Will Implement A,B,C Minimize The Number Of Product

Answer 1

The student's question is about constructing a truth table for given Boolean functions A, B, and C, designing ROM and PLA circuits based on these functions, and minimizing the PLA product terms for an efficient design.

Step-by-step explanation:

The problem at hand involves creating a truth table for three Boolean functions A, B, and C, designing corresponding circuit implementations using read-only memory (ROM) and programmable logic array (PLA), and optimizing the number of products in the PLA circuit. The Boolean functions A, B, and C are defined using minterms or specific combinations of logic operations.

For the ROM implementation, each row of the truth table corresponds to an address in the ROM, with the output being the bit pattern representing the values of functions A, B, and C for that particular combination of inputs X, Y, and Z. The size of the ROM depends on the number of rows in the truth table, which is determined by the number of input variables (in this case, 23 = 8).

In the case of the PLA, the goal is to minimize the number of product terms. This involves identifying common product terms between functions A, B, and C and combining them to reduce the overall complexity of the PLA design. Techniques such as Karnaugh maps or Quine-McCluskey algorithm can be employed to achieve minimization.