2. A Table (Partially Completed) With a list of Basic Identities of. Boolean Algebra is appended to the end of the examination booklet.

Transcription

1 I -. ; I-.,. -. SCUji Instructr: Lcatin: Shawki M, Areibi. DOG (RICH 2520)/SAS Date: Time: Saturday, Octber 29th 2016 _ 11:30-1:00 PM Duratin: 90 minutes. Type: R-C1Clsed Bk." Instructins: L There are 5 questins in ttal, answer all questins. I 2. A Table (Partially Cmpleted) With a list f Basic Identities f. Blean Algebra is appended t the end f the examinatin bklet. 3. The ttal number f pages in the examinatin bklet is 15 pages. Please ntify the invigilatr immediately if yur examinatin bklet des nt cntain the number f pages indicated. 4. Yu have t use Pens (n pencils allwed)! 5. Write yur answers directly n the examinatin bklet. ========N=a=m=e========:I==_ ======Id=n=u=m=b=e=r=======1 Fr use f examiner mark pt f Questin 1 5 Questin 2 5 Questin 3 5 Questin 4 5 Questin 5 5 Ttal, 25 1 f 15

2 '-. ENG 2410, Fall 2016 Midterm Exam Name: _ Questin 1. Lgic Gates [5 marks] Part A. Blean Functins [5 marks] Given the fllwing Blean Functin (SOM): F(A, B, C) = L:m(O, 1,4,5) and assuming that A is MSD and C is LSD. L Write the Blean expressin in terms f A, B,C variables f the SOM (N simplificatin).. ii. Use DeMrgan's Therem t derive the Cmplement (i.e., F) f the Blean expressin f F yu wrte in (i). iii. Simplify the Baleanexpressian fr Fusing identities (Use the Blean Identities Table appended t this exam). iv. Give the simplified Blean expressin f F by using Karnaugh Maps (Shw yur steps!) A BL,1-113 C I G:i) F AGC -tfl BC BCCA-+A) i.jsc:.. (demit'fv 1 B c. + 15L B Cc -tc) 13 e t -s t; i.-., i,.; ;, ':. 2 f 15

3 j ENG 2410, Fall 2016 Midterm Exexa Name: '---' Cntinue Slutin f Questin 1.. F= B 3 f 15

4 .. l - ENG 2410, Fall 2016 Midterm Exam Name: Questin 2. Lgic Design [5 marks] Part A. Car Security System [5 marks] In a car security system, we usually want t cnnect the siren in such a way that the siren will activate when it is triggered by ne t mre sensrs. In additin, there will be a master switch t turn the system n r ff. Let us assume that there is a car dr switch D, a vibratin detectr. switch V, and a master switch M. Assume that when the dr is pened, D=l,therwise Similarly, when the car is being shaken, V=l, therwise, D=O. v=.. We want the siren S t turn n (i.e., set S = 1) when either the dr is pen r the car is shaken. The siren shuld turn n nly when the system is turned n. Hwever, when we turn ff the system, we d nt want the siren t turn n regardless f the state f the dr switch r the vibratin switch. Given the abve descriptin f a car security system, yu are required t build a digital circuit that meets the specificatins listed abve. i. Start by cnstructing a truth table.. ii. Obtain the BleanExpressin in terms f M, D, V frm the truth table as a Sum f Minterms (N simplificatin) Draw a circuit diagram f the Blean Expressin derived in (ii) (N simplificatin). IV. Simplify the Blean expressin btained abve in (ii). 5 f 15

5 ENG 2410, Fall 2016 Midterm Exam Name: ' Cntinue Slutin f Questin 2... i., :t) M D V i Cl ---C i 0 l ,, ( r: I,:, ' - _. v t "-"" "---'. ", _C)_v r t,-_0---:1 d Cl 0 6 f 15

6 ENG 2410, Fall 2016 Midterm Exam Name: _ Questin 3. Cmbinatinal Lgic Design [5 marks] Part A. Decders & Multiplexers [5 marks]. A cmbinatinal circuit is specified by the fllwing tw Blean functins:, Fl(A, E, C) =I:m(l, 4; 7) F2(A, E, C) = IT M(O, 4, 6, 7) i. Implement the circuit using 2-t-4 line Decders with enable. Shw yur cnnectins in detail. ii. Implement the circuit again using 4-t-l line Multiplexers. Shw yur cnnectins in detail. cd III IJ,- I,.J:, tl 05(.. TlZJO,.. ' l ->.-+---C-- :(;)- /, ---- ō D L( 05 t _ Db 01 G l Q )0 1) 02 tn Ot, Os D0 )l -,r -0. (t '-. 8 f 15

7 ENG 2410, Fall 2016 Midterm Exam Name:_'--- _... Cntinue Slutin f Questin A PJ L, = l 0 c) i i I Z v (,1;,1) Z ({1(3,;5) d} C I C 'JI :] 0 ( - c }C t 0 1:}0 l I I -:r> IMt t-l. J 51C Lt _ " f V X C. -A 0 - C 4 _-re - 'u>i r -- c. C----t, c. e; 9 f 15

8 ENG 2410, Fall 2016 Midterm Exam Name:-,- --,- Questin 4. Cmbinatinal Lgic [5 marks ] Part A. Essential Prime Implicants [5 marks] Given the fllwing Blean Functin: F(A, B, C, D) = IIM(l, 4, 6,12,14) Assume A t be the MSD and D t be the LSD. i. Give an expressin fr F as Sum f Minterms instead f the prvided Prduct f Maxterms given abve. ii. Map the minterms n a K-Map. iii. Determine all Prime Implicants (write each ne f them). iv. Determine which f the Prime Implicants is Essential (explain why it is essential. v. Give the simplified Blean expressin fr F. DO NOT DRAW THE CIRCUIT. _@... 'I.,.: 0..5,' '". t... '" "- q 10 Ii ;3, / / I,' c)0 0 0 l 0. (.-,.l --.. t:...-,j "- r... I. "- I,. I 1 i - i I f - I --0. / 'f'i'. { v.q.,1fw. "'<.,,,-{M

9 ENG 2410, Fall 2016 MidtermExam Name:_-'--_----'-_- Questin 5. Universal Gates [5 marks] Part A. NAND Gates [5 marks] i.prve algebraically that NAND gate(s) can be used t implement an OR gate (draw the circuit). ii. Implement a 4-input NAND gate using 2-input NAND gates nly!. m. Given' the Blean expressin: F = A(.8 + C) + E(D + BC). Implement the abve Blean functin (i.e., draw the circuit). F using AND, OR gates Cnvert the circuit implemented abve t all NAND gates. Avid any duplicate gates in yur circuit. (1) =D-- A v (.'M e1e,d:, c...ie.,'{. 'irut use, ue. -'"/''Q(V 4;: hw-re..i'i( A B : ATB. D- -- CL, b. c...l L -+ CL u -- c.d, 13 f 15

10 ENG 2410, Fall 2016 Midterm Exam Name: ---: Cntinue Slutin 01 Questin 5... r "A ( B -t Z) -t F ( 0 -t be) b c r -, I CD { l CCVVe'(L " 0 c&j. N AND _ I'q,,-(e AND w-' AND-flT _ «"-fccce. 0 Z tall +h N T - 0 IZ., _ c-ltec.k 11",; <cve,'6,vbie IS CCMff5",led w (".v.crt'- :JID"), ' ' i r:. I f.9 /.. ;,- e - c f 15