Draw the logic diagram for the function

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Reference no: EM132268819

Fundamentals of Digital Design Questions -

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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:

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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:

Speed (S)

S < 5000 rpm

0

S ≥ 5000 rpm

1

Pressure (P)

P ≤ 200 psi

1

P > 200 psi

0

Temperature (T)

T > 180oF

0

T ≤ 180oF

1

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.

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Note - All equations/proofs, must be typed using an equation editor, such as WORD, or using an inserted table with suitable formatting.

Attachment:- Assignment File.rar

Reference no: EM132268819

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Reviews

len2268819

3/28/2019 9:41:38 PM

All work must be TYPED: All equations/proofs, must be typed using an equation editor, such as WORD, or using an inserted table with suitable formatting. The corresponding theorem must be listed alongside each line of the proof. For tables, use the “insert table” function. For schematics/logic diagrams you must use a schematic software/PowerPoint etc … handwritten diagrams will not be graded. SHOW ALL WORK and ALL Algebraic steps.

len2268819

3/28/2019 9:41:32 PM

You must turn in a hard copy at the beginning of class on the due date. Print using only one side of the page. Double-sided submissions will not be graded. All problems should have a space between questions so that there is room to make comments (skip a line). Written work (scanned) will not be graded. Each page, except the frontispiece, must be numbered. You must have a frontpage (frontispiece) containing only: Your name, ID #, Assignment number, Date assigned and date submitted, Course name & Course number and Professor’s name.

len2268819

3/28/2019 9:41:24 PM

You must use the “header” or “footer function” so that your name, ID#, assignment number is visible on each page. Late submission: A letter grade will be subtracted for late submission. A further letter grade will be subtracted for each day a submission is overdue. Points will be deducted for sloppy work (clearly label inputs, gates, intermediate outputs, and final outputs, diagrams should be large enough to read clearly). Points will be deducted if Axioms/Theorems are not stated when simplifying (IE: if you use 1+A = 1, then the side bar should read Identity: 1+A=1 etc), or if you skip steps in your algebra.

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