sample_test1_sol - Test #1 (SOLUTIONS) Student ID number...

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Unformatted text preview: Test #1 (SOLUTIONS) Student ID number Last name of student First name of student Email address Exam Rules: This is a 1 hour and 50 minutes exam The syllabus includes all material covered until Lecture/Activity 6 This is an Open Book and Notes Exam You are not allowed to consult any other student You may NOT use a calculator, laptop, palmtop, PDA, or such other computer If you need more space, continue on the back sides of pages, but make sure to indicate a continuation ' —--- mmm Representmg Number & Boolean Algebra K—maps Tlmmg Loglc Functions Symbol Dlagrams Representation, Arithmetic r I - (9(0me ‘0”) W M W) 1 I ECSE-2660 Computer Components and Operations, Fall 2000 Page I of 6 1. (25 points) Representations of Logic Functions l a. (5 points) Fill up the following truth table representing G(a,b, c) = (E + b + c) o (a + c) o b C See (7\ have) d. (5 points) Prepare an espresso input file representing G(a, b, c): 3 swam '”’ 22% W’ lo I W": ' V" t 3 * P8 ath‘al’NM F 000 0 P o I l l 37 (I) C; '1 Full "31AI ' \t 0 \ o t l l l l l l f - l l l - e. e. (5 points) Sketch a logic circuit that implements G(a, b, c) using NOR gates on/ly. ~ C\ 9 Lat/law} + CR+C)+ b @7348” "W M» 5)“ ECSE-2660 Computer Components and Operations, Fall 2000 Page 2 of 6 2. (25 points) Number & Symbol Representation, 0 _ l Arithmetic l0 a. (10 points) Convert the number 37210 to binary representation using no more than’oits. Show your work. I l 1 i I. » ls’é i '3": 93 13: ca :2» 232 u j ; rt r : 2/v/' 371/2" Z ‘2 {46 3: j, ‘3: / ‘ 2,, - 4/ ‘Yzfv'j I i "E ' V V c c”, v v v} I v I / c) ; . o Row-u m M 9 372,0 .: lo ll )0 I00 ' A=FF 9/0”“ 5w 3:71:11: ialculate the difference A — B, and B -— A. Show our work. c. (5 points) Given that the ASCII representation of “T” is 5416, find the ASCII representation of “control—T.” Express your answer as a hexadecimal number. ‘cw—iflw M 2 W W oo’o’oo CASCH ifiox 7fb?t W W ECSE-2660 Computer Components and Operations, Fall 2000 Page 3 of 6 3. (20 points) Boolean Algebra a. (10 points) Simplify the following Boolean function to sum-of-products form using the laws of Boolean algebra. Make sure to name or state the laws that you choose to use. f(a,b,c,d)=(a+§b) + c é ‘. : (a +319) 9 Z Mé‘faamj m ‘ Mfr Watch/1w #2 5A,? 4— 323 5&LL’JSW‘ ’ \Qph’ '. W“ J ’ QM > m ()5 Ml QW' ; (15+ be h. (10 points) Given two variables x and y, we can define their exclusive-OR as follows: x S y = x y + i y where the symbol “9” denotes the exclusive—OR of x and y. Using this definition, and the laws of Boolean algebra, prove the following equivalence: X(Y®Z) = Ky 63 xz; Mama): marzhewxz). “17 “jirmyz: wffit§j+<2rj)(”3) (’ ”*-"-“ 49?} [\WW “Id $331115? T- )Lyfivr n32 + )Lfi J1 .— M W; 9152+sz2 9932 +73 92' ECSE-2660 Computer Components and Operations, Fall 2000 Page 4 of 6 4. (20 pomts) Systematic Minimization with K- Maps Consider the following K—map for a Boolean function F(A,B,C,D). The X’s denote don’t care terms. a. (I points) Derive the minimum sum of products (SOP) expression for F(A,B,C,D). ECSE-2660 Computer Components and Operations, Fall 2000 Page 5 of 6 ...
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sample_test1_sol - Test #1 (SOLUTIONS) Student ID number...

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