University of California, Berkeley – College of Engineering Department of Electrical Engineering and Computer Sciences Spring 2007 Instructor: Dr. Dan Garcia 2007-03-05 CS61C Midterm ☺ After the exam, indicate on the line above where you fall in the emotion spectrum between “sad” & “smiley”... Last Name First Name Student ID Number Login cs61c- Login First Letter (please circle) a b c d e f g h i j k l m Login Second Letter (please circle) a b c d e f g h i j k l m n o p q r s t u v w x y z The name of your SECTION TA (please circle) Aaron Alex Brian David Matt Michael Valerie Name of the person to your Left Name of the person to your Right All the work is my own. I had no prior knowledge of the exam contents nor will I share the contents with others in CS61C who have not taken it yet. (please sign) Instructions (Read Me!) • Don’t Panic! • This booklet contains 7 numbered pages including the cover page. Put all answers on these pages; don’t hand in any stray pieces of paper. • Please turn off all pagers, cell phones & beepers. Remove all hats & headphones. Place your backpacks, laptops and jackets at the front. Sit in every other seat. Nothing may be placed in the “no fly zone” spare seat/desk between students. • Question 0 (1 point) involves filling in the front of this page and putting your name & login on every front sheet of paper. • You have 180 minutes to complete this exam. The exam is closed book, no computers, PDAs or calculators. You may use one page (US Letter, front and back) of notes and the green sheet. • There may be partial credit for incomplete answers; write as much of the solution as you can. We will deduct points if your solution is far more complicated than necessary. When we provide a blank, please fit your answer within the space provided. You have 3 hours...relax. Question 0 1 2 3 4 5 Total Minutes 1 36 36 36 36 36 180 Points 1 15 14 15 15 15 75 ScoreName: _______________________________ Login: cs61c-____ 2/7 Question 1: Is this the best midterm in memory? No, we freed it! (15 pts, 36 min) a) I have N bits to represent data, and every bit pattern has a unique meaning. I want to represent 3 times as many things. How many more bits do I need? b) We are given two nibbles, A (=0xF) and B (=0b0010), and we wish to calculate their SUM = A + B. We only have a nibble to store the SUM result. What is SUM if all three nibbles (A, B, SUM) were… Algorithm: SUM = encode( decode-into-decimal(A) + decode-into-decimal(B) ) SUM (single hex character) Decimal number SUM encodes Was there overflow? …sign magnitude?0x …ones complement?0x …unsigned?0x …twos complement? 0x ...encoded with a bias of 7 (like the 0x way the exponent is encoded w/float) c) Put the following in chronological order. We’ve started it for you. Code and Data from various places are stitched together. 1 A CS61C student is assigned a project that implements big_nums. Execution begins at main. The student writes his or her code in C. Link tables are produced. MAL is translated into TAL. Static, code, and global space are reserved/initialized in memory. The student’s C code is translated into MIPS. Links are “edited” d) Assume we have just enough bits to byte-address 51210 zebibytes. We want to define some number of the most-significant bits to encode 910 x 250 things, and some number of the least-significant bits to encode 2,00010 things. How many things can we encode with the remaining bits? Use IEC language, like “16 mebithings”. Show your work. Static Stack Heap 1 typedef struct bignum { 2 int len; 3 char *num; 4 char description[100]; 5 } bignum_t; 6 bignum_t *res; 7 8 int main() { 9 bignum_t b; 10 b.num = (char *) malloc (5 * sizeof(char)); e) For every line of code on the right, we want to know if any memory is used, and if so, where and how much. If zero, leave it blank. // more code belowName: _______________________________ Login: cs61c-____ 3/7 Question 2: If swimming in the 616+17 Cs, keep “a float” (14 pts, 36 min) The figure below shows the layout of the different types of 32-bit float numbers on a not-to-scale real number line (with zero in the center, and NaNs considered to be further from zero than infinity). For each of the (a-f) values below, draw marks below the number line (like we’ve done for 0) indicating where the value would fall. Label the mark with the corresponding letter and actual value below it. a) The sign magnitude number closest to ∞. b) The result of casting the double number closest to -∞ (but is not -∞) into a float. c) 1/(X+1), where X is the largest ones complement number. d) The number represented by the float bits 0x80000001. e) The number represented by the float bits 0x00000000 times the number represented by the float bits 0xFFFFFFFF (using normal floating point multiply mul.s) f) The difference between the int value closest to -∞ and the float that can most closely represent that int’s value. g) The default float rounding mode often needs to break ties for numbers that fall between floats it can represent. What is the largest unsigned int that falls exactly between two floats, and what does it round to? (e.g., If this were in decimal, you might write “3.5 4”). Show your work below, and put your answer in the box. You may leave your result as a (simplified) expression. Negative Zero Positive Zero Least negative denorm Least positive denorm Most negative denorm Most positive denorm Least negative normalized number Least positive normalized number Most negative normalized number Most positive normalized number Negative Infinity “Least negative” NaN “Least positive” NaN Positive Infinity “Most negative” NaN “Most positive” NaN 0 Sign bit: 1 Sign bit: 0Name: _______________________________ Login: cs61c-____ 4/7 Question 3: Goodness, Grandma, what bignums you have! (15 pts, 36 min) Part A: After your extensive C bignum experience, you were hired by Lawrence Berkeley Labs to make an arbitrary precision math package. The scientists use scientific notation and keep track of significant figures. The scientists have written a function called sci_bignum_cmp as shown below. Unfortunately, the implementation has at least one bug. In the boxes at the bottom, briefly explain all of them and give sample
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