HW5_wt_answer (1)

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Oregon State University, Corvallis *

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437

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Mechanical Engineering

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Apr 3, 2024

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pdf

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4

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HW5 - MFGE 437 1. DeMorgan’s Theorems are: Theorem 1: (AB)’ = A’ + B’ Theorem 2: (A+B)’ = A’B’ DeMorgan’s Theorems are useful since all logical operations (even those which we have not discussed in class): NAND, NOR, XOR, etc. can be reduced to combinations of NOT and AND functions or combinations of NOT and OR functions. Thus, with only the three functions (AND, OR, and NOT), you can work out every type of logic operation! a) Use truth tables to show the left and right hand side of Theorem 1 are equal for every combination of A and B ( Show your work using two truth tables, one for each side – be sure each table has the same set of inputs. ): (10 pts.) Partial answer is provided below. (AB)' A B AB (AB)' 0 0 1 0 0 1 1 1 Partial answer is provided below. A'+B' A B A' B' A'+B' 0 0 1 0 0 1 1 1 b) Use truth tables to show the left and right hand side of Theorem 2 are equal for every combination of A and B ( Show your work using two truth tables, one for each side – be sure each table has the same set of inputs. ): (10 pts.) Partial answer is provided below. A'B' A B A' B' A'B' 0 0 1 0 0 1 1 1
HW5 - MFGE 437 Partial answer is provided below. (A+B)' A B A+B (A+B)' 0 0 1 0 0 1 1 1 2. Use truth tables to show the left and right hand side of the following Simplification Theorem are equal for every combination of inputs: (20 pts.) a) A’B’+AB’+AB=A+B’ Partial answer is provided below. A B A`B` AB` AB A`B+AB`+AB A+B` 0 0 1 0 0 1 1 1 THE LAST TWO COLUMNS ARE EQUAL b) ABC+A’BC+A’BC’=BC+A’B Partial answer is provided below. A B C ABC A`BC A`BC` BC A`B ABC+A`BC+A`BC` BC+A`B 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1 THE LAST TWO COLUMNS ARE EQUAL 3. Corvallis Chemical Company is designing a new filling station to transfer liquid chemicals from their production process to tanker trucks. The chemicals are contained in a large holding tank and emptied from there into the trucks. You must design the logic control for the pump motor used for the tanker truck filling system in ladder logic using the truth table approach.
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