A game uses three sensors. A red light (R) in the game switches on if all of the following conditions are true:
sensor D is off
sensor L is on
sensor W is on.
Complete the logic circuit for this game. You must use the correct symbols for the logic gates.
How to approach this question
1. **Analyze the conditions:**
* "sensor D is off": This means we need the logical opposite of D, which is NOT D. This requires a NOT gate for input D.
* "sensor L is on" and "sensor W is on": These inputs are used as they are.
* "**all** of the following conditions are true": The word "all" implies an AND condition. We need a gate that outputs true only when all its inputs are true. This is an AND gate.
2. **Construct the circuit:**
* Draw an input line for D and connect it to a NOT gate.
* Draw input lines for L and W.
* Take the output from the NOT gate (which is NOT D), the input line for L, and the input line for W, and connect all three to the inputs of a single 3-input AND gate.
* Connect the output of the AND gate to the output R.
Full Answer
The problem states that the red light R turns on if (D is off) AND (L is on) AND (W is on).
- **"D is off"** translates to the Boolean expression `NOT D`. In a circuit diagram, this is represented by a NOT gate.
- **"L is on"** and **"W is on"** are represented by the inputs L and W directly.
- **"all ... are true"** translates to the Boolean operator `AND`. This is represented by an AND gate. Since there are three conditions to be met simultaneously, we need a 3-input AND gate.
The final logic circuit is constructed as follows:
1. The input D goes into a NOT gate.
2. The output of this NOT gate, along with the inputs L and W, all feed into a 3-input AND gate.
3. The output of the AND gate is R.
The Boolean expression for this circuit is `R = (NOT D) AND L AND W`.
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Common mistakes
✗ Using the wrong logic gate symbols (e.g., American vs IEC standard if not specified, but consistency is key).
✗ Using an OR gate instead of an AND gate.
✗ Forgetting the NOT gate for input D.
✗ Using three separate 2-input AND gates instead of one 3-input AND gate.