HW5_wt_answer (1)

pdf

School

Oregon State University, Corvallis *

*We aren’t endorsed by this school

Course

437

Subject

Mechanical Engineering

Date

Apr 3, 2024

Type

pdf

Pages

Uploaded by EarlField7390

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.

HW5 - MFGE 437 The pump motor control relay is controlled by the following sensors: • A: Position sensor to sense if the truck is in position. This sensor is a normally closed weight sensor. • B: Limit switch in the holding tank to sense whether there is enough chemical to fill a tanker truck. This switch is a normally open sensor. • C: Limit switch on the filler tube nozzle to sense whether the chemical level in the tanker is at the proper level (to sense if the tanker is filled). This switch is a normally open sensor. • CR: The pump motor control relay (CR), which is normally open. The pump motor should turn on when the tanker is in position and there is a proper amount of chemical in the holding tank. The pump motor should turn off when the tanker is full. (You would normally also have an emergency stop, but we are neglecting it in this problem for simplicity.) 1. Construct the truth table to evaluate the effect of each set of input conditions on the output (pump motor control relay). ( 15pts ) 2. Convert the truth table into a Boolean expression. Simplify the expression. ( 15pts .) 3. Draw the ladder logic rung to control the pump motor control relay (CR). (10 pts.) There are 2 acceptable solutions. You would need to show how you eventually got any of these solutions to get the full 30pts. Solution 1: Solution 2:

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

HW5 - MFGE 437 4. For the following circuit: i) write out the corresponding Boolean expression, ii) simplify the expression ( show your work ), iii) draw the simplified logic circuit. ( 15+15 +10 pts.) The final logic circuit would look like below. You still would need to answer all sections of the question above to get 30points. A C B