John and Jane Doe have eating out they will go sildren, Soc and Sor. When restaurant that serves only hamburgers or one that serves only thicken. Befire going out the family votes to decide on the restaurant. The majority wins, except when Mom and Dad ugror, and in that case they G4, Mom and Dad) win. Any other tie vites produce a trip the chicken restaurant. Design a logic circuit that will autoesstically select the restaurant when everyone votes. Let I represent a vote cast for hamsagers sagers and and a a represe cant for chicken. Follow the design procedure outlined below Complete the truth table for the viting creat
The Correct Answer and Explanation is :
To design the logic circuit for determining which restaurant the family will choose based on their votes, we need to construct a truth table, which will help map the family members’ votes to the final outcome.
Step 1: Define Inputs
Let the following represent the family members’ votes:
- I represents a vote for hamburgers.
- C represents a vote for chicken.
Since the family consists of 4 members (John, Jane, Soc, and Sor), we will define 4 variables representing their individual votes:
- ( J ) for John’s vote
- ( A ) for Jane’s vote
- ( S ) for Soc’s vote
- ( O ) for Sor’s vote
So, we need a truth table with these 4 inputs and the corresponding output representing the selected restaurant. We assume the voting rules based on the information you provided:
Voting Rules:
- If there is a majority vote for hamburgers or chicken, that wins.
- If Mom (Jane) and Dad (John) agree, their choice takes precedence.
- If there is a tie between the votes, the chicken restaurant wins.
Step 2: Construct the Truth Table
We’ll create a truth table with all combinations of votes. Since there are 4 members, there will be ( 2^4 = 16 ) possible combinations of votes.
For each combination:
- Output “Hamburgers” (H) when the majority votes for hamburgers.
- Output “Chicken” (C) when the majority votes for chicken.
- If Mom and Dad agree (even if the other two disagree), output “Hamburgers” if they vote for hamburgers, and “Chicken” if they vote for chicken.
- If there’s a tie and no clear majority, default to “Chicken.”
Step 3: Construct Logic Expressions
From the truth table, we can derive the logic expressions for each scenario. The output will be based on the following logic conditions:
- If Mom and Dad agree: Output their choice.
- If Mom and Dad disagree and the majority is for hamburgers: Output hamburgers.
- If there’s a tie: Output chicken.
I’ll now construct the truth table and logic circuit design based on these rules.
Here’s the detailed truth table based on the voting rules and inputs. Each row represents a possible combination of votes from John (J), Jane (A), Soc (S), and Sor (O), and the resulting output for the selected restaurant.
| J (Hamburger) | A (Hamburger) | S (Chicken) | O (Chicken) | Majority | Mom and Dad Agree? | Output (Restaurant) |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | Tie | No | Chicken |
| 0 | 0 | 0 | 1 | Chicken | No | Chicken |
| 0 | 0 | 1 | 0 | Chicken | No | Chicken |
| 0 | 0 | 1 | 1 | Chicken | No | Chicken |
| 0 | 1 | 0 | 0 | Chicken | No | Chicken |
| 0 | 1 | 0 | 1 | Chicken | No | Chicken |
| 0 | 1 | 1 | 0 | Chicken | No | Chicken |
| 0 | 1 | 1 | 1 | Chicken | No | Chicken |
| 1 | 0 | 0 | 0 | Hamburger | No | Hamburger |
| 1 | 0 | 0 | 1 | Hamburger | No | Hamburger |
| 1 | 0 | 1 | 0 | Hamburger | No | Hamburger |
| 1 | 0 | 1 | 1 | Hamburger | No | Hamburger |
| 1 | 1 | 0 | 0 | Hamburger | Yes (Dad and Mom Agree) | Hamburger |
| 1 | 1 | 0 | 1 | Hamburger | Yes (Dad and Mom Agree) | Hamburger |
| 1 | 1 | 1 | 0 | Hamburger | Yes (Dad and Mom Agree) | Hamburger |
| 1 | 1 | 1 | 1 | Hamburger | Yes (Dad and Mom Agree) | Hamburger |
Explanation:
- Majority Voting:
- If the majority votes for hamburgers, the output is hamburgers. If the majority votes for chicken, the output is chicken.
- In cases where the vote is split evenly, the family defaults to choosing chicken, as per the rules.
- Mom and Dad Agreement:
- If John (Dad) and Jane (Mom) agree on their vote, the restaurant choice will be based on their decision, overriding the other votes.
- For example, when both John and Jane vote for hamburgers, regardless of Soc and Sor’s votes, the output will be hamburgers.
- Tie Votes:
- If there is no clear majority and no agreement between Mom and Dad, the vote will go to the chicken restaurant.
Logic Circuit Design:
Using the truth table, we can now design the logic circuit for this voting system. The circuit will be based on these conditions:
- Majority Rule: This can be determined using majority gates or by counting how many 1’s (Hamburger votes) there are.
- Agreement Rule: If both John and Jane vote the same, we output their vote (this can be implemented using AND gates).
- Tie and Default to Chicken: This can be achieved using an OR gate to detect ties or situations where no clear majority exists.
By combining these gates, we can implement a logic circuit that will automatically select the correct restaurant based on the family votes.