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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
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I ECSE2660 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)“ ECSE2660 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 Rowu 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 ECSE2660 Computer Components and Operations, Fall 2000 Page 3 of 6 3. (20 points) Boolean Algebra
a. (10 points) Simplify the following Boolean function to sumofproducts 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 exclusiveOR 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' ECSE2660 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). ECSE2660 Computer Components and Operations, Fall 2000 Page 5 of 6 ...
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