NATIONAL UNIVERSITY OF SINGAPORE CS2100 COMPUTER ORGANISATION

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1 S NATIONAL UNIVERSITY OF SINGAPORE SHOOL OF OMPUTING MID-TERM TEST AY6/7 Semester S OMPUTER ORGANISATION 8 March 7 Time Allowed: hour 3 minutes INSTRUTIONS. This question paper contains T () questions (excluding the bonus question) and comprises NINE (9) printed pages.. An Answer Sheet, comprising TWO () printed page, is provided for you. 3. Write your Name, Matriculation Number and Tutorial Group Number on the Answer Sheet with a P. 4. Answer ALL questions within the space provided on the Answer Sheet. 5. You may write your answers in pencil (at least B). 6. Submit only the Answer Sheet at the end of the test. You may keep the question paper. 7. This is a LOSED BOOK test. However, an A4 single-sheet double-sided handwritten reference sheet is allowed. 8. Maximum score is 4 marks. 9. alculators and computing devices such as laptops and PDAs are not allowed.. Pages 7 and 8 are for your rough work. They contain blank truth tables, K-maps and state table for your use.. Page 9 contains the MIPS Reference Data sheet. D OF INSTRUTIONS

2 S Bonus question:. [This is the bonus question which is worth mark. The mark of this question will only be added if the total mark scored is less than 4.] On nd February 7, Aaron shared a story in his lecture about cookies. What is the title of that story? A. Four-and-three-quarter cookies B. Six-and-a-half cookies. Seven cookies D. How to cook cookies like a booky rooky E. I have a cookie I have a monster ah, cookie monster! F. I think this must be a trick question. He didn t tell any story on that day, but he nearly fainted as he didn t take any cookies on that day. uestions 5: Each multiple-choice-question has only one correct answer. Write your answers in the boxes on the Answer Sheet. Two marks are awarded for each correct answer and no penalty for wrong answer.. Given the following hexadecimal representation in IEEE 754 single-precision floating-point number system: B What decimal value does it represent? A B D E. None of the above.. Given the following MIPS code fragment, encode the bne instruction. (The MIPS Reference Data sheet is provided on page 9.) here: addi $t, $t, add $t, $t, $t bne $t, $t, here A. 5AFFFE B. 548FFFE. 548FFFD D. 5AFFFD E. None of the above. S Mid-term Test - of 9 - AY6/7 Semester

3 S 3. What is the following Boolean expression in M form? F3(W,X,Y,Z) = Y' W + Y' Z + Z' Y X A. F3(W,X,Y,Z) = M(,, 3, 4, 7,,, 5) B. F3(W,X,Y,Z) = M(, 5, 6, 8, 9,, 3, 4). F3(W,X,Y,Z) = M(,, 8, 9,,, 3, 4) D. F3(W,X,Y,Z) = M(,, 3, 4, 5,,, 4) E. None of the above. 4. Simplify the following expression of a 5-variable Boolean function. m's are the minterms and M s the maxterms. A. B.. M987 D. m895 E. M987 + m895 (m35 M987 m5) + m895 (M + M68) 5. You are given a 4 decoder with -enable and active high outputs, and a -bit magnitude comparator, as shown below. S S 4 DE 3 -bit OMP X X<Y X=Y Y X>Y Which of the following Boolean functions can be implemented using either or both of the above devices without any additional logic gate? Note that complemented literals are not available. Logical constants and are always available. (i) F5a(A, B,, D) = A B ' (ii) F5b(A, B,, D) = m(,,3) (iii) F5c(A, B,, D) = m(,3,5,7) A. Only (i). B. Only (i) and (ii).. Only (i) and (iii). D. Only (ii) and (iii). E. All of (i), (ii) and (iii). S Mid-term Test - 3 of 9 - AY6/7 Semester

4 S uestions 6 : Write your answer in the space provided on the Answer Sheet. You do not need to show workings, unless otherwise stated. 6. [5 marks] (a) How many PIs (prime implicants) and EPIs (essential prime implicants) are there in the K-map of the function below? Note that X denotes don t-care values. [ marks] F6a(A, B,, D) = m(3, 4, 5, 7,, 4) + X(, 6, 8,, 5) (b) Given the following magnitude comparator, write the Boolean function F6b(A,B,,D) in m form. [3 marks] A B D D D bit OMP X Y X<Y X=Y X>Y F6b 7. [6 marks] The following sequential circuit cycles through 6 states AB. Two states are unused. The circuit is implemented using a JK flip-flop for A, a D flip-flop for B, and a T flip-flop for. J K lk ' A D lk ' B T lk ' LK On the answer sheet, complete the state diagram by filling in the state numbers which are in decimal, as well as the state transition from the unused state. Two states ( or in decimal, and or 6 in decimal) have been filled for you. S Mid-term Test - 4 of 9 - AY6/7 Semester

5 S 8. [5 marks] Implement the following function using a single 4: multiplexer with at most one additional logic gate. omplemented literals are not available. F8(A, B,, D) = M(,,, 5, 9, 3) 9. [8 marks] Study the following circuit which uses a half adder, a 4 decoder with -enable and active high outputs, and three devices each with a -enable control (): A (+)-device: it takes in two inputs P and and produces 3-bit output with value P++. A (+)-device: it takes in two inputs P and and produces 3-bit output with value P++. A ( )-device: it takes in two inputs P and and produces 3-bit output with value (P+). A B X Y HA S S S 4 DE 3 (+) P (+) P T T T T T T 4: MUX 3 4: MUX 3 X Y ( ) P T T T 4: MUX 3 Z The above circuit is too complex. Redesign the circuit using the minimum number of logic gates. Write your expressions for X, Y and Z (6 marks) and draw the logic diagram of your circuit ( marks). omplemented literals are not available. S Mid-term Test - 5 of 9 - AY6/7 Semester

6 S. [6 marks] Study the MIPS code below, given that $s and $s have been assigned the starting addresses of integer arrays A and B respectively. You need to determine the value of $s after the code is executed. The MIPS Reference Data sheet is provided on page 9. addi $s, $zero, addi $t, $s, addi $t, $s, addi $t4, $zero, addi $t5, $zero, 4 loop: beq $t4, $t5, out lw $t, ($t) lw $t3, ($t) beq $t, $zero, out beq $t3, $zero, out bne $t, $t3, notequal add $s, $s, $t notequal: addi $t4, $t4, 4 add $t, $s, $t4 add $t, $s, $t4 j loop out: What is the value of $s after the code is executed, given the following arrays? (a) A = {,, 3, 4, 5, } B = {,, 3, 4, 5, } [ marks] (b) A = { -9, -3, -5,, -4, } B = { -6, -3, -7,, -4, -8 } [ marks] (c) A = { 3, -, 7, 5, 9, -4, 6, 6, -3,, 7, } B = { 5, -, 7, -3, 9, -4, 6,, 3, 8, 7, } [ marks] D OF PAPER (Blank truth tables, K-maps and state table are provided in the next two pages.) S Mid-term Test - 6 of 9 - AY6/7 Semester

7 S This page is for your rough work. A B D A B D A B D S Mid-term Test - 7 of 9 - AY6/7 Semester

8 S This page is for your rough work. A B S Mid-term Test - 8 of 9 - AY6/7 Semester

9 S S Mid-term Test - 9 of 9 - AY6/7 Semester

Question Total Possible Test Score Total 100

Question Total Possible Test Score Total 100 Computer Engineering 2210 Final Name 11 problems, 100 points. Closed books, closed notes, no calculators. You would be wise to read all problems before beginning, note point values and difficulty of problems,