A farmer named Mr. Sijamba has a large dog which is part wolf, a goat, and several heads of cabbage. In addition, the farmer owns a north barn and a south barn. The farmer, dog, cabbages, and goat are all in the south barn. The farmer has chores to perform in both barns. However, if the dog is left with the goat when the farmer is absent, he will bite the goat, and if the goat is left with the cabbages, it will eat them. To avoid disaster, Mr. Sijamba asks you to build a small portable computer system having four switches, representing the farmer, dog, goat, and cabbages. If a switch is connected to a battery (V1), the character represented by the switch is in the south barn; if the switch is connected to ground (V2), the character is in the north barn. The output of the computer system goes to a lamp, which is to light whenever there is an impending disaster. Thus the farmer can go about his chores, using the computer system to tell him what he must take with him from one barn to another in order to avoid trouble.
TASK: in groups of 4:
(a) Design the computer system and build it using logic gates.
(b) Write a Truth Table for all the possibilities. Indicate a disaster by the symbol L = 1. Transfer the Truth Table data onto a Karnaugh Map and simplify the L-Function.
(c) Implement the simplified L-Function using basic logic gates.
Answer (2)
To solve this problem, we will design a logic circuit and create a truth table to prevent any disaster in Mr. Sijamba's barns. Let's break down the task step-by-step:
(a) Designing the Computer System Using Logic Gates :
Define Variables : Assign a switch for each character:
F (Farmer)
D (Dog)
G (Goat)
C (Cabbages) Each switch can be either 1 (in the south barn) or 0 (in the north barn).
Conditions for Disaster :
Disaster occurs if the Dog (D) and Goat (G) are alone together without the Farmer (F is 0 and D and G are both 1).
Disaster occurs if the Goat (G) and Cabbages (C) are alone together without the Farmer (F is 0 and G and C are both 1).
Logic Expression :
To indicate a disaster, L = 1.
The logic sum of the two disaster conditions can be expressed as: L = F ⋅ D ⋅ G + F ⋅ G ⋅ C
Implementing the Logic Gates : You will use basic logic gates (AND, OR, NOT) to implement the L function based on the above expression.
(b) Write a Truth Table :
Create rows for all possible combinations of F, D, G, and C (16 possibilities since each has two states, thus 2 4 = 16 ). Here's a simplified version:
FDGCL011010111100111...............
Only the rows where disaster occurs are filled with 1 in L.
(c) Simplify Using a Karnaugh Map and Implement :
Create a Karnaugh Map using the truth table values for L.
Simplify using grouping:
Group 1s together to get the simplest form.
The simplified function remains L = F ⋅ G ⋅ ( D + C )
Use Logic Gates to build this:
Use NOT gates for F .
AND gates for ( F ⋅ G ) and ( ( D + C ) requires an OR gate).
A final AND gate to combine the results.
This step-by-step plan provides Mr. Sijamba with a logic system to monitor and prevent the disaster scenarios in his barns by indicating when the local environment sets up a potential problem.
Mr. Sijamba's logic system uses switches to represent a farmer, dog, goat, and cabbages, ensuring he avoids disastrous combinations. We derived a logic expression and created a truth table showing when disaster occurs, leading to a simplified logic function using gates. This setup will allow Mr. Sijamba to monitor conditions in the barns effectively.
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