The statements that are true are:

a. Implementing full adder using PLAs utilizes all the minterms provided by the AND array: This is true. A full adder has three inputs and two outputs. The AND array in a PLA can be used to generate all the eight minterms of the three inputs. These minterms are then used by the OR array to implement the sum and carry outputs of the full adder.

c. The PLA is programmed by connecting the output of the AND gate to the input of the OR if the corresponding minterm produces a 1: This is true. In a PLA, the AND gates are used to generate minterms. If a minterm is part of the sum-of-products expression for a particular output, the output of the corresponding AND gate is connected to the input of the OR gate for that output.

e. The number of OR gates required to implement an N-input and P-output truth table is equal to P: This is true. Each output of a truth table is implemented by an OR gate in a PLA. Therefore, the number of OR gates required is equal to the number of outputs.

The statements that are false are:

b. The number of AND gates required to implement an N-input and P-output truth table is equal to the number of minterms in the first column of the truth table: This is false. The number of AND gates required is equal to the number of minterms in the truth table, not just the first column.

d. PLAs require fewer gates to implement any logic function than are needed by the minimal form of the same logic function: This is false. While PLAs can be more efficient than some other forms of logic implementation, they do not always require fewer gates than the minimal form of the same logic function. The number of gates required depends on the specific function and its minimal form.

Question

The statements that are true are:

a. Implementing full adder using PLAs utilizes all the minterms provided by the AND array: This is true. A full adder has three inputs and two outputs. The AND array in a PLA can be used to generate all the eight minterms of the three inputs. These minterms are then used by the OR array to implement the sum and carry outputs of the full adder.

c. The PLA is programmed by connecting the output of the AND gate to the input of the OR if the corresponding minterm produces a 1: This is true. In a PLA, the AND gates are used to generate minterms. If a minterm is part of the sum-of-products expression for a particular output, the output of the corresponding AND gate is connected to the input of the OR gate for that output.

e. The number of OR gates required to implement an N-input and P-output truth table is equal to P: This is true. Each output of a truth table is implemented by an OR gate in a PLA. Therefore, the number of OR gates required is equal to the number of outputs.

The statements that are false are:

b. The number of AND gates required to implement an N-input and P-output truth table is equal to the number of minterms in the first column of the truth table: This is false. The number of AND gates required is equal to the number of minterms in the truth table, not just the first column.

d. PLAs require fewer gates to implement any logic function than are needed by the minimal form of the same logic function: This is false. While PLAs can be more efficient than some other forms of logic implementation, they do not always require fewer gates than the minimal form of the same logic function. The number of gates required depends on the specific function and its minimal form.

Knowee AI · Accepted Answer

The statements that are true are:

a. Implementing full adder using PLAs utilizes all the minterms provided by the AND array: This is true. A full adder has three inputs and two outputs. The AND array in a PLA can be used to generate all the eight minterms of the three inputs. These minterms are then used by the OR array to implement the sum and carry outputs of the full adder.

c. The PLA is programmed by connecting the output of the AND gate to the input of the OR if the corresponding minterm produces a 1: This is true. In a PLA, the AND gates are used to generate minterms. If a minterm is part of the sum-of-products expression for a particular output, the output of the corresponding AND gate is connected to the input of the OR gate for that output.

e. The number of OR gates required to implement an N-input and P-output truth table is equal to P: This is true. Each output of a truth table is implemented by an OR gate in a PLA. Therefore, the number of OR gates required is equal to the number of outputs.

The statements that are false are:

b. The number of AND gates required to implement an N-input and P-output truth table is equal to the number of minterms in the first column of the truth table: This is false. The number of AND gates required is equal to the number of minterms in the truth table, not just the first column.

d. PLAs require fewer gates to implement any logic function than are needed by the minimal form of the same logic function: This is false. While PLAs can be more efficient than some other forms of logic implementation, they do not always require fewer gates than the minimal form of the same logic function. The number of gates required depends on the specific function and its minimal form.

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