Baseball is a complicated game, and often the manager has a difficult time keeping track of all the rules of thumb that guide decisions. To assist your favorite baseball team, you have been asked to design a logic circuit that will flash a light when the manager should give the steal sign. The rules have been laid out for you by a baseball fan with limited knowledge of the game as follows: Give the steal sign if there is a runner on first base and
a. There are no other runners, the pitcher is right-handed, and the runner is fast; or
b. There is one other runner on third base, and one of the runners is fast; or
c. There is one other runner on second base, the pitcher is left-handed, and both runners are fast.
Under no circumstances should the steal sign be given if all three bases have runners. Design a logic circuit that implements these rules to indicate when the steal sign should be given.
Analysis:
The table below lists the 8 possible conditions under which the steal sign should be given, using the following logic notations:
A runner on a base is 1, no runner is 0
A fast runner on a base is 1, a non-fast runner is 0
A right-handed pitcher is 1, a left-handed pitcher is 0
From this final expression, a logic circuit diagram can be made to achieve the correct response:
Note: The circles in the figure are nodes, not inversions.
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