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Figure P1318
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1319 Baseball is a complicated game and often the
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manager has a dif cult 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 ash 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 rst 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
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Section 3: Logic Design 1324 Find the logic function corresponding to the truth
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table of Figure P1324 in the simplest sum-of-products form
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A 0 0 0 0 1 1 1 1
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B 0 0 1 1 0 0 1 1
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C 0 1 0 1 0 1 0 1
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F 1 0 0 0 1 0 1 1
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1320 A small county board is composed of three
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commissioners Each commissioner votes on measures presented to the board by pressing a button indicating whether the commissioner votes for or against a measure If two or more commissioners vote for a measure it passes Design a logic circuit that takes the three votes as inputs and lights either a green or red light to indicate whether or not a measure passed
Figure P1324
1325 Find the minimum expression for the output of
the logic circuit shown in Figure P1325
1321 A water puri cation plant uses one tank for
chemical sterilization and a second larger tank for settling and aeration Each tank is equipped with two sensors that measure the height of water in each tank and the ow rate of water into each tank When the height of water or ow rate is too high the sensors produce a logic high output Design a logic circuit that sounds an alarm whenever the height of water in both tanks is too high and either of the ow rates is too high, or whenever both ow rates are too high and the height of water in either tank is also too high
A B C F(A, B, C, D) D
Figure P1325
1322 Many automobiles incorporate logic circuits to
alert the driver of problems or potential problems In one particular car, a buzzer is sounded whenever the
1326 Use a Karnaugh map to minimize the function
f (A, B, C) = ABC + ABC + ABC
13
Digital Logic Circuits
a Build the Karnaugh map for the logic function de ned by the truth table of Figure P1327 b What is the minimum expression for this function c Realize F using AND, OR, and NOT gates
Input B
Output F 0 0 0 1 0 0 1 x
A 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
B 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1
C 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1
D 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
F 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 1
0 0 1 1 0 0 1 1
0 1 0 1 0 1 0 1
Figure P1330
1331 Design a logic circuit which will produce the
one s complement of an 8-bit signed binary number
1332 Construct the Karnaugh map for the logic
function de ned by the truth table of Figure P1332, and nd the minimum expression for the function
A 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
B 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1
C 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1
D 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
F 1 0 1 0 0 0 0 1 1 0 1 0 1 1 1 0
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