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Problem Set 5
Out: 22 March
Due: Wednesday (beginning of class), 29 March
Collaboration Policy - Read Carefully (similar to PS4)
For this assignment, you may work on your own or with any one other person of your choice except for anyone you worked with on PS3 or PS4. If you work with a partner, you should turn in one assignment with both of your names on it. If you would prefer to be assigned a partner, send email to firstname.lastname@example.org before 5pm on Friday, 24 March (include any constraints or preferences you have on your assigned partner). If a suitable match requests a partner, you will receive a partner assignment. Partners will be assigned using a greedy algorithm based on when requests arrive, so you are more likely to receive a suitable partner assignment if you send in your request early.
You may consult any outside resources including books, papers, web sites and people you wish, except you may not copy code from other big number representation implementations. There are many implementations of big numbers in C available on the web (for example, there is one in the Python interpreter and GMP), and it would certainly defeat the purpose of this assignment if you copied one of them instead of thinking on your own. You may look at design documents for big integer implementations is you wish, but we recommend thinking about your own design first, and only looking for other designs if you are really stuck.
You are also encouraged to discuss these problems with students in the class. You must acknowledge any people and outside resources you work with on your assignment. If you discuss the assignment with people other than your partner, you may not take any written materials out of your discussion. It is fine to bounce ideas off other people, but the answers you turn in must be your own.
You are strongly encouraged to take advantage of the staffed lab hours posted on the CS216 web site.
Here, we will consider a simple hypothetical smart card with one 8-bit register using big-endian encoding. The current used for each operation scales linearly with the number of bits in the register that flip (either a 0 becomes a 1, or a 1 becomes a 0). The card implements a simple counter: the value in the register increases by one each clock tick. So, if the register initially contains 0000 0011 after the next clock ticks the resuting value in the register will be 0000 0100 and 3 units of current will have been consumed.
Your goal is to determine the number stored in the register, just by observing the current consumed by the card.
2. What is the fewest number of additional clock tick current readings that could be enough to uniquely determine the exact value stored on the card?
(Note that the product of any two numbers ending in 9 should end in a 1, so Excel must be wrong. The number on the bottom line is the current US national debt to give a sense that numbers of this scale could meaningfully occur in spreadsheets.)
For the next questions your goal is to design and implement a variable length integer implementation that is more accurate than Excel's.
The desired properties are:
bignum bignum_create (char *p_x); /* post: returns a bignum object representing the value p_x where p_x is a decimal number represented as a string */ char *bignum_unparse (bignum p_b); /* post: returns a string representation of p_b that shows its decimal value */
bignum bignum_add (bignum p_b1, bignum p_b2); /* post: returns a bignum representing the value p_b1 + p_b2 */
bignum bignum_mult (bignum p_b1, bignum p_b2); /* post: returns a bignum representing the value p_b1 * p_b2 */
printf ("%s\n", bignum_unparse (bignum_mult (bignum_create ("99999999"), bignum_create ("99999999"))));to demonstrate that your number representation is more accurate than Excel's.
The submission program will run your bignum implementation on several test cases and check it produces the correct answers. Submitting your code electronically is not a substitute for turning in your answers (including all your bignum implementation code) on paper.
CS216: Program and Data Representation
University of Virginia
Using these Materials