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Two logic inputs, A and B, feed into the logic circuit shown in Figure 1 - AQA - A-Level Physics - Question 1 - 2018 - Paper 8

Question 1

Two logic inputs, A and B, feed into the logic circuit shown in Figure 1. The logic output from the circuit is Q. Deduce the Boolean expression for the output of th... show full transcript

Worked Solution & Example Answer:Two logic inputs, A and B, feed into the logic circuit shown in Figure 1 - AQA - A-Level Physics - Question 1 - 2018 - Paper 8

Step 1

Deduce the Boolean expression for the output of this logic circuit

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Answer

The logic circuit consists of the following operations:

The inputs A and B are first fed into an AND gate. This operation can be expressed as: $A \cdot B$
The output of the AND gate is also fed into a NOT gate (inverter), which yields: $\overline{A \cdot B}$
Additionally, A is fed into another NOT gate, producing: $\overline{A}$
The output from the first AND operation ( $A \cdot B$ ) and the output from the NOT gate with input A ( $\overline{A}$ ) are then combined using an OR gate: $Q = (A \cdot B) + \overline{A}$

Thus, the Boolean expression for the output is:

$Q = (A \cdot B) + \overline{A}$

Step 2

Complete the truth table

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Answer

To complete the truth table, we will systematically evaluate the inputs A and B ( using the logic gates from Figure 1:

When A = 0 and B = 0:
- C = 0 (from AND gate), D = 1 (from NOT gate), E = 0 (from AND gate with D and B), Q = 0.
When A = 0 and B = 1:
- C = 0 (from AND gate), D = 1 (from NOT gate), E = 0 (from AND gate with D and B), Q = 0.
When A = 1 and B = 0:
- C = 0 (from AND gate), D = 0 (from NOT gate), E = 0 (from AND gate with D and B), Q = 0.
When A = 1 and B = 1:
- C = 1 (from AND gate), D = 0 (from NOT gate), E = 1 (from AND gate with D and B), Q = 1.

The completed truth table is:

| A | B | C | D | E | Q |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 0 | 1 | 1 |

Step 3

Suggest two benefits of using the logic circuit in Figure 2

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Answer

Less Complex Circuit: The logic circuit in Figure 2 is simpler and easier to manufacture. A simpler design typically leads to lower production costs and a more reliable circuit.
Fewer Integrated Circuits (ICs): Figure 2's configuration uses fewer ICs compared to Figure 1. Fewer ICs can result in reduced power consumption and overall size, making the circuit more efficient in terms of power and space usage.

Step 4

State the single logic gate that would perform the same logic function as the circuits shown in Figure 1 and Figure 2

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Answer

The single logic gate that would perform the same logic function as the circuits in Figure 1 and Figure 2 is the EOR (Exclusive OR) gate.

Two logic inputs, A and B, feed into the logic circuit shown in Figure 1 - AQA - A-Level Physics - Question 1 - 2018 - Paper 8

Worked Solution & Example Answer:Two logic inputs, A and B, feed into the logic circuit shown in Figure 1 - AQA - A-Level Physics - Question 1 - 2018 - Paper 8

Deduce the Boolean expression for the output of this logic circuit

Complete the truth table

Suggest two benefits of using the logic circuit in Figure 2

State the single logic gate that would perform the same logic function as the circuits shown in Figure 1 and Figure 2

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