2020exam1-1

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ECE 2020-C Fundamentals of Digital Design Spring 2022 5 Problems, 8 pages Exam One 16 February 2022 1 This exam will be conducted according to the Georgia Tech Honor Code. I pledge to neither give nor receive unauthorized assistance on this exam and to abide by all provisions of the Honor Code. Signed (With your Full Legal Name): Instructions: Instructions: This is a closed book, closed note exam. Calculators are not permitted. If you have a question, raise your hand and I will come to you. Please work the exam in pencil and do not separate the pages of the exam. For maximum credit, show your work. Good Luck! Your Name (please print): ________________________________________________ For maximum (and partial) credit, show your work. Good Luck! 1 2 3 4 5 total 20 20 20 20 20 100

ECE 2020-C Fundamentals of Digital Design Spring 2022 5 Problems, 8 pages Exam One 16 February 2022 2 (This page intentionally left blank)

ECE 2020-C Fundamentals of Digital Design Spring 2022 5 Problems, 8 pages Exam One 16 February 2022 3 Problem 1 (5 parts, 20 points) Fundamentals Part A (12 points) Convert the following notations using the minimum required number of digits. Binary Notation Decimal Notation 100011 23 Binary Notation Octal Notation Hexadecimal Notation 10110011 42 Part B (2 points) Which one of the following fundamental Boolean algebra operators performs a logical multiplication? a) NOT b) AND c) OR d) XOR Part C (2 points) The duality principle states that any theorem or identity in Boolean algebra is also true if 0s and 1s and then AND and OR operators are swapped throughout. a) True b) False Part D (2 points) Which one of the following statements about CMOS transistor switches is NOT true? a) Two ideal switches connected in series implement the AND operator. b) nMOS transistors transmit logic level 0 well and logic level 1 poorly when CLOSED. c) High impedance is a state where a transistor switch is CLOSED. d) The impedance of a transistor switch is on the order of 100MΩ when it is OPEN.

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ECE 2020-C Fundamentals of Digital Design Spring 2022 5 Problems, 8 pages Exam One 16 February 2022 4 Problem 1 Cont. (5 parts, 20 points) Fundamentals Part E (2 points) Which of the following networks is invalid? Circle all that apply. a) b) c) d)

ECE 2020-C Fundamentals of Digital Design Spring 2022 5 Problems, 8 pages Exam One 16 February 2022 5 Problem 2 (2 parts, 20 points) Boolean Algebra Part A (12 points) Transform the following Boolean expression to a form where it is ready for switch-level implementation. In other words, convert it to a format where there are complement bars over only input variables, not over operations. The behavior of the expression should remain unchanged. Do not implement. Out A1 = A ̅ + B ̅̅̅̅̅̅̅ ∙ C + D ̅̅̅̅̅̅̅ ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ Out A2 = (A ̅ + B) ∙ (C ̅ ∙ (D + E ̅ )) ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ∙ F ̅ ∙ G ̅̅̅̅̅̅ Part B (8 points) Given the Boolean algebra equation: Out B (A, B, C) = BC ̅ + AB ̅ + A ̅ BC a) (4 points) Give the truth table for Out B . b) (2 points) Give the canonical product of sums (POS) Boolean representation for Out B. c) (2 points) Give the canonical sum of minterms ( ∑(𝒊)) representation for Out B .

ECE 2020-C Fundamentals of Digital Design Spring 2022 5 Problems, 8 pages Exam One 16 February 2022 6 Problem 3 (4 parts, 20 points) Switched Networks For each partial switch network below, draw the missing pull-up or pull-down network so that the circuit contains no floats or shorts. Assume both inputs and their complements are available. Also, write the Boolean expression computed by the completed circuit. (The expression should have complements only over the individual input signals, not over subexpressions.) Do not simplify the equations. Out A = _______________________________________________________________________________________________ Out B = _______________________________________________________________________________________________

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ECE 2020-C Fundamentals of Digital Design Spring 2022 5 Problems, 8 pages Exam One 16 February 2022 7 Problem 4 (2 parts, 20 points) Mixed Logic Reengineering Part A (10 points) Write the output expression for the gate design shown above. Also determine the number of transistors used in its implementation. 𝑂?? ? = ________________________________________________________________________________ 𝑂?? ? = ________________________________________________________________________________ # ??𝑎??𝑖????? = _____________________________________________________________________ Part B (10 points) Now reimplement these expressions using NAND gates and inverters. Determine the number of transistors used in this implementation. # ??𝑎??𝑖????? = _____________________________________________________________________ Problem 5 (2 parts, 20 points) Karnaugh Maps

ECE 2020-C Fundamentals of Digital Design Spring 2022 5 Problems, 8 pages Exam One 16 February 2022 8 Part A (10 points) Simplify the following product-of-sums (POS) expression using a Karnaugh Map. Circle and list all prime implicants, indicating which are essential, and write the sum-of-products (SOP) expression. F(A, B, C, D) = ∏(4,5,6,10,11,14,15) Prime Implicants: 1. ____________________ 2.____________________ 3.____________________ 4.____________________ 5.____________________ 6.____________________ 7.____________________ Essential? Y or N? Y or N? Y or N? Y or N? Y or N? Y or N? Y or N? Simplified SOP expression Part B (10 points) Given the following Karnaugh Map, circle and list all prime implicants, indicating which are essential and write the simplified product-of-sums (POS) expression. Prime Implicants: 1.____________________ 2.____________________ 3.____________________ 4.____________________ 5.____________________ 6.____________________ 7.____________________ Essential? Y or N? Y or N? Y or N? Y or N? Y or N? Y or N? Y or N? Simplified POS expression