ࡱ> XZW` %bjbjss hYG$<<<P<4,=X>Z6@6@6@6@AAAQQQQ;QUX$_Zh\BXAAAAABX6@6@WX]G]G]GAd6@6@Q]GAQ]G]G]G6@> eN1<uD<]GG< mX0X]GU]ETU]]GU]]G(AA]GAAAAABXBXGXAAAXAAAA7<< Student Name: ______________________ Student Number:_____________________ EE2504 EXAMINATION 1 Spring Form A Instructions: Read and follow the instructions carefully. 1. Do not open the examination until the instructor tells you to do so. 2. This is a closed book, closed notes examination. No calculators of any kind may be used. 4. This examination will be machine graded. Print your NAME, COURSE, STUDENT NUMBER, FORM and DATE on the top of the OPSCAN sheet. 5. Encode your STUDENT NUMBER and FORM on the OPSCAN sheet by filling in exactly one circled number or letter under each symbol. 6. Since this exam will be machine graded, the following instructions must be followed exactly: a) Use a Number 2 pencil only. b) Make sure all marks are heavy and dark. c) Make any erasures completely clean. Do not leave any smudges. d) Do not make a mark in more than one circle for each question. 7. Check the projection screen for additional instructions and information. 8. The cover sheet of this examination booklet and the OPSCAN sheet must be turned in. 9. I have neither given nor received any aid while working on this examination. I have not used a calculator nor referenced any material while working on this examination. Signature _____________________________ (Blank Page) 1. Convert 3B.116 into binary. 1) 111011.0001 ***2) 111011.13) 1110114) 110011.15) 1111110.0016) 111011.111...7) None of the above 2. Convert 25.22510 to hexadecimal. 1) C9.CCC...2) C9.C3) 19.3999...***4) 19.35) 11001.2246) 31.147) None of the above 3 Obtain the 2's complement of 0000. 1) 0000 ***2) 100003) 11114) 00015) 10006) None of the above 4. An 8-bit register stores integer numbers in signed 2's complemented form. What is the range of the numbers which can be stored in the register. 1) 0 ~ 2552) -127 ~ 1273) -128 ~ 127 ***4) -128 ~ 1285) None of the above 5. Perform the binary arithmetic of the two 6-bit numbers in signed 2's complement form. (Note that the result should be in signed 2's complement form.) 101011 - 100110 = ? 1) 1110012) 0011013) 10001014) 000101 ***5) 1110116) 0001107) None of the above 6. Two positive numbers in signed 2's complement form are to be added. An overflow occurs if 1) Carry into the sign bit is 1. *** 2) Carry into the sign bit is 0. 3) Carry out of the sign bit is 1 4) Carry out of the sign bit is 0. 5) None of the above 7. A 32-bit register stores a floating-point number in IEEE single precision format. Find the equivalent decimal number represented by the register whose content is BF40000016. 1) -1.12) -0.153) -0.1 x 21264) -1.1 x 21265) -0.75 ***6) -0.117) -0.558) None of the above 8. A decimal number +3.25 is to be stored in a register in IEEE single precision format. Find the content of the register in hexadecimal. 1) CFD0 00002) 5FD0 00003) 3FD0 00004) 4058 00005) 40D0 00006) 4050 0000 ***7) None of the above 9. A 32-bit register stores the smallest number represented in IEEE single precision format. Find the content of the register in hexadecimal. Note: -1.0 x 21 > -1.1 x 21 -1.0 x 21 > -1.0 x 22 1) 807F FFFF2) FFFF FFFF ***3) FF80 00004) 8070 00005) 8000 00006) None of the above 10. A valid identity is ... 1) (xy)' = x'y'2) x(y+z) = xy + z3) x + 0 = 04) y + xy' = x + y ***5) x + yz = (x+y)z6) x + x' = 07) xx' = 18) None of the above 11. The logic function of the circuit given below is ...  EMBED Word.Picture.8  1) x + y2) x' + y3) x' + y'4) x + y'5) x'y6) xy7) xy' ***8) x'y'9) None of the above 12. A function has 3 variables, x, y and z. Find a minterm of the function from the given choices. 1) x + y + z2) x'y'z ***3) xy4) x5) x' + y' + z6) y7) None of the above 13. A function f(x,y,z) = x  EMBED Word.Picture.8  y  EMBED Word.Picture.8  z, where  EMBED Word.Picture.8  is Exclusive-OR operation. Find f(x,y,z) in the sum of minterm form. 1)  EMBED Word.Picture.8 (0,1,2,3)2)  EMBED Word.Picture.8 (0,1,2,4,5)3)  EMBED Word.Picture.8 (4,5,6,7)4)  EMBED Word.Picture.8 (3,4,5,6,7)5)  EMBED Word.Picture.8 (0,3,5,6)6)  EMBED Word.Picture.8 (1,3,5,7)7)  EMBED Word.Picture.8 (0,2,4,6)8)  EMBED Word.Picture.8 (1,2,4,7) ***9)  EMBED Word.Picture.8 (0,2,4,6,7)10) None of the above 14. We know that any logic functions can be expressed in canonical SOP (Sum-Of-Product) form or canonical POS (Product-Of-Sum) form. Is it true that any logic functions can be implemented by using only 2-input NAND gates? 1) Yes ***2) No3) Not enough information 15. Find the logic function implemented by the circuit given below.]  EMBED Word.Picture.8  1) (x + y + z) (w + x' + y) (w' + z) *** 2) (x' + y' + z') (w' + x + y') (w + z') 3) xyz + wx'y + w'z 4) x'y'z + w'xy' + wz' 5) None of the above 16. Simplify the function f with don't cares d. f(w,x,y,z) =  EMBED Word.Picture.8 (0,1,2,8,9.12,13) d(w,x,y,z) =  EMBED Word.Picture.8 (7,10,11,14,15) 1) w + x'y + x'yz'2) wy' + x'y' + wyz + w'x'z'3) wy' + x'yz'4) w + x'y'5) w + x'y' + x'z' ***6) w + w'x'7) wx + x'z'8) None of the above 17. A logic function f(w,x,y,z) =  EMBED Word.Picture.8  (1, 3, 7, 8, 9, 10, 11, 14, 15) is given. Simplify the function in POS (Product-Of-Sum) form. 1) (w + x') (w + y) (y + z) (x' + z) 2) (w' + x) (w' + y') (y' + z' ) (x + z') 3) (x + y') (w' + z') 4) (x' + y) (w + z) *** 5) (x + y') (w + z) 6) (x' + y) (w' + z') 7) None of the above For the next two problems, consider the FF given below.  EMBED Word.Picture.8  18. Find the characteristic table of the FF. (1)(2)(3)(4)(5)(6)(7) A BQ(t+1)Q(t+1)Q(t+1)Q(t+1)Q(t+1)Q(t+1)0 00Q'(t)1Q(t)Q(t)1None0 1Q(t)0Q'(t)10Q(t)of1 01Q(t)0Q'(t)Q'(t)0them1 1Q'(t)1Q(t)01Q'(t)*** 19. The current state of the FF is 0. Show all the possible input combinations of A and B which make the next state of the FF to 1. 1) AB = 0X ***2) AB = X03) AB = 1X4) AB = X15) AB = 00 only6) AB = 11 only7) AB = 01 only8) AB = 10 only9) None of the above20. The speed of a computer is ultimately determined by ... (Choose the best answer.) 1) Fan-out limit of gates 2) Propagation delay of gates *** 3) Noise margin of gates 4) Power dissipation of gates 5) Logic types of gates 6) Complexity of gates 21. We want to build a circuit which turns on a light for odd numbers, number 0 and number 6. The number is coded in 2421 code. Let (a,b,c,d) represents the bits for an input whose corresponding number is obtained as 2a+4b+2c+1d. Only the input combinations given in the table are applied to the circuit. When the output of the circuit f is 1, the light is turned on. a) Fill in the following truth table. (5 points) a b c doutput f0 0 0 0 0 0 0 10 0 1 00 0 1 10 1 0 01 0 1 11 1 0 0 1 1 0 11 1 1 01 1 1 1 b) i) Fill the Karnaugh map. Use x for don't cares. ii) Show the groups of minterms to be combined. iii) Show the product term associated with each group. iv) Obtain the simplified function f.  EMBED Word.Picture.8  f = You have to turn in both the cover sheet of this exam booklet and the OPSCAN sheet. Make sure that you have put your name and id on the OPSCAN sheet.     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