Reference no: EM132277018
Fundamentals of Digital Design Assignment -
All equations/proofs, must be typed using an equation editor, such as WORD, or using an inserted table with suitable formatting. Show all work and all Algebraic steps.
For Questions 1-4:
I. Draw the logic diagram for the function.
II. Derive the Karnaugh map for the function.
III. Write the function in Sum of Products notation.
IV. Simplify the expression.
V. Draw the logic diagram for the simplified function.
VI. Show that the simplified expression equals the original equation by deriving the truth tables for both, and, give a gate delay justification of why this is the simplest circuit.
5. Use Boolean Algebra to prove, by simplifying BOTH sides of the equation, that:
6. A water-well pump is automatically turned on if the water level is low in any two or more of three reservoirs. The water-level detectors in each reservoir generates a logical '0' if the water-level is low. Design a logic system that turns on water by generating a logical '1' in response to inputs received from the three level detectors: Use, X1, X2, X3, to denote the corresponding water-level detectors: [Hint ON = 1].
a. Derive the canonical equation for the system.
b. Draw the Gate Level schematic (logic diagram) for the circuit.
c. Simplify the expression using a K-map and Boolean Algebra.
d. Draw the Gate Level schematic (logic diagram) for the simplified circuit.
e. Use truth tables to show that both expressions are equivalent, highlight the the input combinations that activate the system and, give a gate delay justification of why this is the simplest circuit.
7. An Aircraft is equipped with a safety system that turns on a warning light when a certain combination of engine speed, pressure, and temperature occur, as per the below table:
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Speed (S)
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S < 5000 rpm
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0
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S ≥ 5000 rpm
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1
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Pressure (P)
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P ≤ 200 psi
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1
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P > 200 psi
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0
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Temperature (T)
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T > 180oF
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0
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T ≤ 180oF
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1
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The warning light, W, is turned on by a logical '1,' and is governed by the following equation:
w = [P + S-]T-
a. Draw the Gate Level schematic (logic diagram) for the circuit.
b. Derive the truth table for the circuit.
c. Determine whether the warning light is on when:
I. Speed = 6250 rpm, Pressure is 280 psi, and Temperature is 150oF
II. Speed = 740 rpm, Pressure is 180 psi, and Temperature is 200oF
8. A computer circuit performs a logic operation upon a 3-bit binary number A2A1A0, where A2 is the MSB and A0 is the LSB. The Rocket will launch whenever GO = '1.' Based on the system equation below:
i. Draw the Gate Level schematic (logic diagram).
ii. Construct the truth table.
iii. Determine which decimal values will result in a launch.
Note - Need the assignment typed in a word diagram with an original gate diagram and a simplified gate diagram. Please use word, PowerPoint or Photoshop to complete the diagrams.
Attachment:- Assignment Files.rar