ECE 2030 -- Introduction to Computer Engineering EXAM #1 February 16, 2011 Page 1 of 6 Name: Student Number: 1. Check that your exam includes all 6 pages. 2. PRINT your name and student number in the spaces above. 3. Read all instructions and problems carefully. Points may be deducted for failure to follow instructions. 4. Show ALL of your work on these pages. If you need extra space for a particular problem, write on the back of the previous page. 5. You are NOT permitted to use notes, books, calculators, or other resources during this exam. 6. This exam lasts for 75 minutes. Point values are listed for each problem to assist you in best using your time. 7. Institute policy prohibits the posting of student grades using an identifiable key (name, student number, etc.). If you wish to have your scores posted on the course website so that you can check them, please sign on the line below and a random identification code will be assigned when the exam is returned. DO NOT WRITE IN THIS BOX SIGNATURE Problem 1. (18 points possible) Problem 2. (15 points possible) Problem 3. (12 points possible) Problem 4. (10 points possible) Problem 5. (20 points possible) TOTAL. (75 points possible)ECE 2030 -- Introduction to Computer Engineering EXAM #1 February 16, 2011 Page 2 of 6 Problem 1. (18 points) A. (14 points) Perform each of the following conversions. Write your answers in the boxes at the right edge. (i) Convert 1010010112 to decimal. (ii) Convert 17310 to binary. (iii) Convert 110011012 to octal. (iv) Convert 5638 to decimal. (v) Convert 6EB16 to binary. (vi) Convert 97510 to hexadecimal. (vii) Convert B1D916 to octal. B. (4 points) Express each of the following values as a decimal number. Write your answers in the boxes at the right edge. (i) 1011.1012 (ii) 72.38ECE 2030 -- Introduction to Computer Engineering EXAM #1 February 16, 2011 Page 3 of 6 Problem 2. (15 points) A. (10 points) In the blank in front of each expression in the left hand column, write the letter (P – Z) corresponding to the equivalent expression in the right hand column. Not all answers in the right hand column will be used and some may be used more than once. (i) _____ F(A, B, C) = Σm (0, 1, 5, 6) P) A B C + A B C + A B C (ii) _____ F(A, B, C) = ΠM (0, 1, 2, 4, 7) Q) A C (iii) _____ (A + B) (A + B + C) (B + C) R) B C D + A B D + A B D (iv) _____ (B + C + D) + (A + B D) + A B D S) A B C + A B C + A B C (v) _____ A C + B (A + D) T) A B + A C + B C U) A B C + A B + B C Z) None of the above B. (5 points) An algebraic expression for a logic function is given below. Using Boolean Algebra, simplify this expression so that (i) only individual literals are complemented, not product or sum terms (e.g., A is allowed, A + B and A B are not allowed) and (ii) no parentheses are needed. Eliminate any redundant terms (e.g., A A, A A, A + 0) that appear during simplification. It is not necessary to show every transformation as a separate step, particularly ones that involve only regrouping or reordering terms. You should include all major transformations and it must be obvious how each expression was derived from the previous one. F = A B + C + ( C + D + A B ) + B + C ( A + D )ECE 2030 -- Introduction to Computer Engineering EXAM #1 February 16, 2011 Page 4 of 6 Problem 3. (12 points) A. (4 points) Given F(A, B, C) = Σm (0, 1, 4, 6), express the function in algebraic sum-of-minterm and product-of-maxterm form. F(A, B, C) = (sum-of-minterms) F(A, B, C) = (product-of-maxterms) B. (4 points) For each function listed below, complete the corresponding truth table. J(A, B, C) = A B + B(A + C) K(A, B, C) = A B C + A(C + B) C. (4 points) Given the function G(A, B, C) defined by the Karnaugh map below, complete the short-hand SOP and POS expressions for this function. G(A, B, C) = Σm ( ) G(A, B, C) = ΠM ( ) A B C K 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 A B C J 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 00 1 0 01 0 1 11 1 1 10 0 1 AB CECE 2030 -- Introduction to Computer Engineering EXAM #1 February 16, 2011 Page 5 of 6 Problem 4. (10 points) A. (8 points) A CMOS switch network is shown below. Complete the truth table for this network, specifying the connectivity functions for the pull-up and pull-down networks, FPU and FPD, and specifying the circuit output as “0,” “1,” “float,” or “short” for each input combination. A B C Fpu Fpd F 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 B. (2 points) Which of the following statements best describes the switch network shown above (based on your truth table)? Circle the number in front of the best response. 1. The switch network is fully complementary and implements the NAND function. 2. The switch network is fully complementary and implements the NOR function. 3. The switch network is fully complementary and implements a logic function other than NAND or NOR. 4. The switch network is not fully complementary. F C B A B A C AECE 2030 -- Introduction to Computer Engineering EXAM #1 February 16, 2011 Page 6 of 6 Problem 5. (20 points) A. (6 points) Given the Karnaugh map below, list ALL of the prime implicants in algebraic form and circle them in the map. For each prime implicant, circle “ess” if it is an essential prime implicant of this function. (You should not need all of the lines provided.) Prime implicants: ess ess ess ess ess ess ess ess ess ess B. (8 points) Write a minimal sum-of-products (SOP) expression for the function defined by the following Karnaugh map. List the essential prime implicants first in your expression. Circle the corresponding terms used in the K-map labeled “Final SOP.” The K-map labeled “work copy” is for your use and will not be graded. work copy Final SOP F(A, B, C, D) = Number of essential prime implicants: C. (6 points) Draw a schematic of a circuit implementing your SOP expression from part B using only NANDs and INVERTERs. Your schematic should have a single connection for each input
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