Question

Need this ASAP, I will thumbs up! Please show work, thank you!

1. Jerry needs to plan for his weekend activity. He may or may not go to play tennis, depending on his friends’ availability. If both Andrew and Bob are going, then Jerry will go with them. Or, if Charlie will go, then Jerry will also go with him. Otherwise, Jerry will not go to play tennis. Please design a logic circuit that makes the decision for Jerry automatically based on his friends’ choices. Use A, B, C to represent the choices of the three friends (Andrew, Bob, and Charlie), respectively, with “1” meaning “will go” and “0” meaning “won’t go”. Use J to represent the decision for Jerry, again with “1” meaning “will go” and “0” meaning “won’t go”.

You need to solve the problem by following the procedure below:

1. Derive a truth table for the decision making system first; Please make sure you use the right symbols for the system’s inputs and output according to the symbols given in the description above. (5 points)

2. Use a Karnaugh map (K-map) to obtain the most simplified sum-of-product Boolean expression for the system. (5 points)

3. Implement the decision making system from step b) into a circuit using the following logic gates only: 2-input AND gate and 2-input OR gate. You can use as many gates as you need. (5 points)

Answer 1

Answer -

As per question John will only go if both Andrew and Bob are going (ie. AB in boolean logic) or if Charlie will go (OR C).

So the corresponding boolean expression for this problem will be J = AB + C

A) Now we will draw the truth table for the above logic, I have made a separate column for AB, but it is done just for easy understanding and to avoid any mistakes. It is good strategy to have separate columns for intermediate values so as to avoid errors while making truth table for complex boolean expressions.

B) In K-map we will write 1 in the blocks which have resultant value of 1 in the truth table otherwise 0. In our case it will be for (1,3,5,6,7). We will try to enclose 8 squares all having 1s, if not possible then try for 4, not possible try 2, so as all 1s are enclosed.

In our case we have enclosed 4 squares and 2 squares. For finding the corresponding boolean product write only those variable which value is 1 for all common rows/columns in enclosed section. If 0 is common the write complement of the variable in expression.

C) Attach AND gate with A and B as its input and then attach its output as input to OR gate for which other input is C. Output of OR gate will be final output.

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