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HW - CS231 Summer 2008 Homework 1...

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CS231 Summer 2008 Homework 1 file:///Users/joshuasmith/Downloads/hw1/hw1.html 1 of 5 6/16/08 2:04 PM CS231 Summer 2008 Homework 1 Due at 5:00pm, Monday, June 23, 2008 in 0212 Siebel Center (in basement) Introductory notes: This homework covers Number systems, Boolean algebra, Minterms, Maxterms, and Karnaugh Maps, from the first 4 lectures. There are a total of 10 questions in the homework worth 100 points. The general guideline for doing assignments is that you must convince us that you know what you're doing. To receive credit, make sure your solutions are neat and legible, and that you show enough work. Write your name , netID , and " CS231 " clearly on the first page. You can discuss homework with the professor or the TA. However, do not look at or copy anyone else's solutions. See the Syllabus for our cheating policy. You must staple all your pages together if you use more than one page. Turn in the assignment at the TA office listed above. You can slide your paper under the door if the office is empty. Do NOT leave your assignment in the bins outside the room. Homework will be accepted up to 2 days late (5:00pm, Wednesday, 6/25/2008), with a 10% penalty for each day late. Book problems marked with a star have solutions available at the book's website . You are encouraged to use these as practice problems. Feel free to ask us questions at office hours or on the newsgroup. Notation: F' means NOT F. So ( A + B )' is the same as: NOT ( A + B ). (10 pts) Show the detailed steps involved in the following base conversions. In each case, solve for X. 11100111 2 = X 10 a. 457121 8 = X 16 b. 1101.011 2 = X 10 c. A7E.F9B 16 = X 8 d. 231 X = 100010100 2 e. 1.
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CS231 Summer 2008 Homework 1 file:///Users/joshuasmith/Downloads/hw1/hw1.html 2 of 5 6/16/08 2:04 PM (10 pts) Show the detailed steps (i.e. borrowing, carrying) involved in the following arithmetic calculations: 1101 2 + 101 2 a. 101011 2 - 10101 2 b. 101 2 x 1101 2 c. E7 16 x A2 16 d. 4B 16 - 2D 16 e. 2. (12 pts) Binary numbers and Boolean algebra What is the decimal equivalent of the largest binary integer that can be obtained with 11 bits i. 25 bits ii. a. Below is a complicated if-then statement written in C. The operators &&, ||, and ! correspond to AND, OR, and NOT, respectively. if ( done || ( found && ! ( done && ! signal ))) { return; } b. Express the condition as a Boolean function. You may abbreviate the terms as D (for done ), S (for signal ), and F (for found ). i. Write the truth table for the function. Include columns for sub-expressions to show your work. ii. Simplify the function as much as possible using Boolean algebra. Indicate the axioms/laws you use at each step. iii. Rewrite the if-then statement using the simplified function. iv. 3. (10 pts) Simplify these functions using the laws of Boolean algebra. Clearly show the steps of your derivations. State which axioms you are using at each step. AC' + AB'C + BC a. (A + B')(A' + B)' b. ABC' + A'C' c. BC' + B(AD' + CD') d. (D'E + C + ED'C)(D'EC' + A(D+E') + AC') e.
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