A farmer owns a 350-acre dairy farm in upstate New York. In addition to milk and butter, the farmer sells fresh eggs at the Union Square Greenmarket in Manhattan. It is imperative that the farmer protects the hen that lays his eggs. He has two barns, one hen, and a supply of corn. A fox has been attempting to eat the hen by hiding in a barn. The hen can move freely from one barn to another. Farmer George sometimes stores corn in one barn and sometimes in the other, but he never stores it in both at the same time. The hen would like to eat the corn and the fox would like to eat the hen. Farmer George decides to design an alarm system to protect the hen and the corn. The design should only use logic gates and include the possible input variables. The alarm will sound if: 1. The fox and the hen are in the same barn, or 2. The hen and the corn are in the same barn.
Question
A farmer owns a 350-acre dairy farm in upstate New York. In addition to milk and butter, the farmer sells fresh eggs at the Union Square Greenmarket in Manhattan. It is imperative that the farmer protects the hen that lays his eggs. He has two barns, one hen, and a supply of corn. A fox has been attempting to eat the hen by hiding in a barn. The hen can move freely from one barn to another. Farmer George sometimes stores corn in one barn and sometimes in the other, but he never stores it in both at the same time. The hen would like to eat the corn and the fox would like to eat the hen. Farmer George decides to design an alarm system to protect the hen and the corn. The design should only use logic gates and include the possible input variables. The alarm will sound if: 1. The fox and the hen are in the same barn, or 2. The hen and the corn are in the same barn.
Solution
To design the alarm system using logic gates, we need to identify the input variables first. In this case, the input variables are the locations of the fox, the hen, and the corn. We can represent these variables as binary inputs:
- F1 and F2: Fox is in barn 1 or barn 2 respectively.
- H1 and H2: Hen is in barn 1 or barn 2 respectively.
- C1 and C2: Corn is in barn 1 or barn 2 respectively.
The alarm should sound if the fox and the hen are in the same barn, or if the hen and the corn are in the same barn. This can be represented as:
- Alarm = (F1 AND H1) OR (F2 AND H2) OR (H1 AND C1) OR (H2 AND C2)
This logic equation can be implemented using AND and OR gates. The AND gates are used to detect if the fox and the hen, or the hen and the corn, are in the same barn. The OR gates are used to trigger the alarm if any of these conditions are met.
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