Question

Consider an apartment that has two bedrooms and a shared hallway to a common area. There is a single hall light and a switch in each room to turn on the hall light. No matter what position each switch is in, flipping either switch turns the hall light on if off, or off if on. Your goal is to design a logic circuit to represent this problem. Define the inputs and outputs and then provide the initial equations that describe your circuit and minimize your output equations using k-maps. Draw your circuits from the minimized equations using AND, OR, and NOT gates.

Now that you’ve designed this circuit can you reduce the number of gates

Answer 1

The goal is to design a logic circuit to represent the problem of controlling a hall light from two switches in different rooms. The inputs are the switch positions and the output is the state of the hall light. The circuit can be implemented using minimized equations and gates like XOR.

Step-by-step explanation:

The goal is to design a logic circuit to represent the problem of controlling a hall light from two switches in different rooms. The inputs in this circuit are the positions of the two switches in the rooms, and the output is the state of the hall light. To represent this, we can use two input variables, A and B, to represent the switch positions, and an output variable, H, to represent the state of the hall light.

The initial equations that describe this circuit are:
A' + B' = H

We can minimize the output equations using Karnaugh maps (k-maps) to simplify the Boolean expressions. By doing so, we can reduce the number of gates required to implement the circuit. The minimized equations for this circuit are:
H = A XOR B

To draw the circuit from these equations, we can use AND, OR, and NOT gates. The circuit would consist of an XOR gate with inputs A and B, and the output of the XOR gate would be connected to the hall light.