Studentenommer: Student number: Volpunte: Full marks: 160 Open / closed book: Oopboek / toeboek: 21 Punt: Mark: BELANGRIK- IMPORTANT

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1 Departement Elektriese, Elektroniese en Rekenaar-Ingenieurswese Department of Electrical, Electronic and Computer Engineering Eksamen Invulvraestel Kopiereg voorbehou Vakkursus ERS November 2007 Examination Fill in paper Copyright reserved Course ERS November 2007 Student se besonderhede: Student's details: Van (opsioneel): Surname (optional): Voorname (opsioneel): First name (optional): Tel. nr. gedurende toetsreeks: Tel no. during test series: Studentenommer: Student number: Tel. nr. na toetsreeks: Tel. no. after test series: Toetsinligting: Test information: Maksimum punte: Maximum marks: 185 Duur van vraestel: Duration of paper: 3 Hours 3 Ure Totale aantal bladsye (hierdie blad ingesluit): Total numer of pages (including this page): 21 Punt: Mark: Volpunte: Full marks: 160 Open / closed book: Oopboek / toeboek: Closed Toe BELANGRIK- IMPORTANT 1. The examination regulations of the University of Pretoria apply. Die eksamenregulasies van die Universiteit van Pretoria geld. 2. No programmable calculators are allowed. Geen programmeerbaar sakrekenaars word toegelaat nie. 3. No notes are allowed. Geen notas word toegelaat nie. 4. Show all calculations. Toon all berekeninge. 5. Complete all the sections. Voltooi al die afdelings. Internal Examiner(s): Interne Eksaminator(e): S. Reddy External Examiner: Eksterne Eksaminator: D. V. Bhatt 1

2 Section A: Multiple Choice [10] Tick the correct box / Tick die korrekte boks: 1. A MSI / IC can contain / n MSI / IC kan bevat a) between 1 and 20 gates. / tussen 1 en 20 hekke. b) between 20 and 200 gates. / tussen 20 en 200 hekke. c) between 200 and 400 gates. / tussen 200 en 400 hekke. d) more than 400 gates. / meer as 400 hekke. a b c d 2. Which of the following descriptions is not true? A combinational logic function can be represented by a / Watter van die volgende beskrywings is nie waar nie? 'n kombinatoriese logiese funksie kan verteenwoordig word deur 'n a) maxterm list using the Σ notation. / maksterme lys deur gebruik te maak van die Σ notasie. b) minterm list using the Σ notation. / minterme lys deur gebruik te maak van die Σ notasie. c) truth table. / waarheidstabel d) Karnaugh map(s). / Karnaugh kaart(e) a b c d 3. If a devices output code has fewer bits than the input code, the device is usually called / As n digitale baan se uitsetkode minder bisse het as die insetkode, dan is die baan n a) a decoder. / n dekodeerder. b) an encoder. / n enkodeerder. c) Neither a) nor b) / Ook nie a) nie nog minder b) a b c 4. A sequential device that normally samples its inputs and changes its output only when a clocking signal is changing is called a / 'n Sekwensiële baan wat normaalweg sy insette versamel en sy uitsette verander, alleelik wanneer 'n geklokde sein verander is genoem 'n a) flip-flop. / wipbaan. b) latch. / grendel c) Either a) or b) / Een van beide a) of b) a b c ERS 220 Exam

3 5. A collection of 2 or more D flip-flops with a common clock input is called a / n Versameling van 2 of meer wip-bane met n gemeenskaplike klok inset word genome n a) counter. / teller b) register / register c) Neither a) nor b) / Ook nie a) nie nog minder b) a b c 6. ROM memory is / ROM geheue is a) a combinational circuit / n kombinatoriese stroombaan b) a sequential circuit / n sekwensiële stroombaan c) both a) and b) / beide a) en b) d) neither a) nor b) / ook nie a) nie nog minder b) a b c d 7. Which statement best describes the behaviour of a Static RAM / Watter verklaring beskryf die gedrag van 'n Static RAM die beste a) The data stored at each location must be refreshed periodically by reading it and then writing it back again, or else it disappears. / Die data gestoor by elke opstelling moet van tyd tot tyd verfris word deur dit te lees en dan terug te skryf, anders verdwyn dit. b) Once a word is written at a location, it remains stored as long as power is applied to the baan, unless the same location is written again. / Sodra n woord geskrywe word by n plek, bly dit gestoor so lank as wat krag aangewend wordtot die baan tensy dieselfde opstelling is weer geskryf word. c) Once a word is written at a location, it remains stored as long as power is applied to the baan and even if the same location is written again. / Sodra 'n woord geskrf word by n plek bly dit gestoor so lank as wat krag aangewend word tot die baan selfs indien dieselfde opstellling weer geskrywe word. d) Once a word is written at a location, it remains stored, even after power is removed. / Sodra 'n woord is geskrywe word by 'n opstelling, bly dit gestoor, selfs nadat krag verwyder is. a b c d ERS 220 Exam

4 8. Which statement best describes the behaviour of a Dynamic RAM / Watter verklaring beskryf die gedrag van 'n Dynamic RAM die beste a) The data stored at each location must be refreshed periodically by reading it and then writing it back again, or else it disappears. / Die data gestoor by elke opstelling moet van tyd tot tyd verfris word deur dit te lees en dan terug te skryf, anders verdwyn dit. b) Once a word is written at a location, it remains stored as long as power is applied to the baan, unless the same location is written again. / Sodra n woord geskrywe word by n plek, bly dit gestoor so lank as wat krag aangewend wordtot die baan tensy dieselfde opstelling is weer geskryf word. c) Once a word is written at a location, it remains stored as long as power is applied to the baan and even if the same location is written again. / Sodra 'n woord geskrf word by n plek bly dit gestoor so lank as wat krag aangewend word tot die baan selfs indien dieselfde opstellling weer geskrywe word. d) Once a word is written at a location, it remains stored, even after power is removed. / Sodra 'n woord is geskrywe word by 'n opstelling, bly dit gestoor, selfs nadat krag verwyder is. a b c d 9. Which of the following ROMs can be written to only one time? / Watter van die volgende "ROMs" kan kan net eenkeer geskryf word? a) EEPROM b) Mask PROM c) (OTP) ROM d) Both b) and c) / beide b) en c) a b c d 10. (DDR) SDRAM can double the data rate of SDRAM by / (DDR) SDRAM kan die data tempo van SDRAM verdubbel deur a) transferring data on the rising edge of the clock only. / verplaas data na die stygende rand van die klok alleen. b) doubling the clock of a standard DRAM and transferring data on the rising edge of the clock only. / verdubbel die horlosie van 'n standaard DRAM en verplaas die data na die stygende rand van die klok alleen. c) transferring data on both edges of the clock, rising and falling. / verplaas data na beide kante van die klok, opstygend en vallend. d) transferring data anytime the clock is positive. / verplaas data enige tyd wat die klok positief is. a b c d ERS 220 Exam

5 Section B: Short Questions [11] 1. A PLA can be programmed to realise any sum-of-products expression, subject to the size limitations of the device. List the 3 limitations. / n PLA kan geprogrammeer word om enige som-van-produkte uitdrukking te besef, onderworpe aan grootte beperkinge van die apparaat. Lys die 3 beperkinge. (3) 2. Draw the general structure of a clocked synchronous Moore state machine. / Skets die algemene struktuur van n geklokte sinkrone Moore toestandsmasjien. (4) 3. Draw the general structure of a clocked synchronous Mealy state machine. / Skets die algemene struktuur van n geklokte sinkrone Mealy toestandsmasjien. (4) ERS 220 Exam

6 Section C: Number Systems And Codes [15] 1. Complete the table below. Use 8 digits to represent each number. / Voltooi die onderstaande tabel. Gebruik 8 syfers om elke getal voor te stel. (10) Decimal / Desimaal 111 Base 2 / Basis 2 Base 5 / Basis 5 Base 7 / Basis 7 Signed Magnitude / Signed Magnitude (Base 2) 1 s Complement / 1 s Komplement (Base 2) 2 s Complement / 2 s Komplement (Base 2) 5 s Complement / 5 s Komplement (Base 5) 7 s Complement / 7 s Komplement (Base 7) 2. Convert the following base 16 number to base 2 and base 8. / Skakel die volgende basis 16 nommer oor na basis 2 en basis 8. (5) 9E36.7A 16 ERS 220 Exam

7 Section D: Digital Circuits [20] 3. The following figure shows a CMOS circuit. / Die volgende figuur toon n CMOS stroombaan. a. Construct a Truth Table (Z = H or L). / Stel n waarheidstabel saam (Z = H of L). (15) A B C Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Z OFF OFF OFF OFF ON ON ON ON ERS 220 Exam

8 b. Draw the logic diagram for the gate represented in (a). / Teken die logiese diagram vir die hek wat in (a) voorgestel word. (5) ERS 220 Exam

9 Section E: Combinational Logic Design Principles [27] 1. Consider the following two logic functions: / Oorweeg die volgende twee logiese funksies: F = Σ QRST (0, 1, 7, 9, 15), and G = Π QRST (2, 3, 9, 11) a) Write down the canonical sum of logic function F. / Skryf die kanonieke som van logies funksie F neer. (3) b) Write down the canonical product of logic function G. / Skryf die kanonieke produk van logies funksie G neer. (3) c) Assume the follwing don t care terms d (6, 8, 14) for logic functions F and G. For functions F and G, use the Karnaugh maps to derive the minimum sum-of-products expressions. / Neem aan dat die volgende don t care terme d (6, 8, 14) vir the logiese funksies F en G bestaan. Deur gebruik te maak van die Karnaugh kaarte, bepaal die minimum som-van-produkte uitdrukking vir die funksies F en G. (8) ERS 220 Exam

10 F = G = d) Use only NAND gates to realise the minimum sum-of-product for logic function F. / Gebruik net NAND hekke om die minimum som-van-produkte vir funksie F te realiseer. (3) ERS 220 Exam

11 2. For the product-of-sums function H below, use the Karnaugh maps to derive the minimum sum-of-products expression. / Vir die produk-van-somme funksie H hieronder, gebruik die Karnaugh diagram om die minimum som-van-produkte uitdrukking af te lei. (10) H = Π PQRST (0, 4, 7, 10, 11, 12, 15, 16, 22, 26, 27, 28, 30 + d(1, 6, 14, 17, 19, 20) H = ERS 220 Exam

12 Section F: Combinational Logic Design Practices [25] 1. Given the following Boolean function / Gegewe die volgende Boolse funksie F = Π VWXYZ (1, 4, 6, 8, 9, 11, 12, 14, 19, 20, 21, 22, 24, 26, 27, 29, 30) Implement function F using two 74x151 MUXs, two inverting gates and one multiple input NAND gate. No other gates may be used. / Implementeer die funksie F deur gebruik te maak van twee 74x151 MUXs, twee omkerende hekke, en een meervoudige inset NAND hek. Geen ander hekke mag gebruik word nie. (15) ERS 220 Exam

13 2. Given the following Boolean function / Gegewe die volgende Boolse funksie F = (A + B + C + D ). (A + B + C + D ). (A + B + C+ D ). (A + B + C + D ). (A + B + C + D ). (A + B + C + D ). (A + B +C + D ). (A + B + C + D ) Implement function F using two 74x138 decoders and one multiple input NAND gate. No other gates may be used. / Implementeer die funksie F deur gebruik te maak van twee 74x138 dekodeerders en een meervoudige inset NAND hek. Geen ander hekke mag gebruik word nie. (10) ERS 220 Exam

14 Section G: Sequential Logic Design Principles [47] 1. The following figure shows a clocked synchronous state machine. / Die volgende figuur toon n geklode sinkrone toestandsmasjien. a) What type of machine is the above sequential circuit? Explain why? / Watter soort masjien is die boonste sekwensiële stroombaan? Verduidelik hoekom? (3) Useful Expressions / Nuttige Uitdrukkings Flip-Flop Characteristic Equations / Wipbaan Karaktertrek Vergelyking Edge Triggered D Flip-Flop Q* = D T Flip-Flop Q* = Q T Flip-Flop with Enable Q* = EN. Q + EN. Q ERS 220 Exam

15 b) Determine the transition and output equations. / Bepaal die oordrag en uitset vergelykings. (12) ERS 220 Exam

16 c) Compile the transition/ output table. / Stel die oordrag/ uitset tabel op. (8) Q1 Q2 Q3 Q1* Q2* Q3* X Y Z ERS 220 Exam

17 2. The following figure shows a state diagram of a clocked synchronous state machine. / Die volgende figuur toon n toestandsdiagram van n geklokde sinkrone toestandsmasjien. EN, 0 A EN, 1 B EN, 1 EN, 0 E EN, 0 H EN, 0 EN, 0 EN, 0 EN, 0 EN, 0 EN, 0 G EN, 0 C EN, 0 EN, 0 F EN, 0 D EN, 0 a) What type of machine is represented by the above state diagram? / Watter soort masjien is verteenwoordig by die boonste toestandsdiagram? (2) ERS 220 Exam

18 b) Compile the state/ output table. / Stel die toestand/ uitset tabel saam. (8) S A B C D E F G H EN 0 1 S*, MAX ERS 220 Exam

19 c) Compile the transition/ output table. / Stel die oordrag/ uitset tabel saam. (6) Q0 Q1 Q EN 0 1 Q0* Q1* Q2*, MAX d) Determine the transition equations Q0*, Q1* and Q2*, and the output equation, MAX. / Bepaal die oordrag vergelykings Q0*, Q1* en Q2*, en die uitset vergelyking, MAX. (8) ERS 220 Exam

20 Section H: Sequential Logic Design Practices [30] 1. Design a circuit with output (QA, QB, QC and QD) sequence 0, 3, 6, 12, 9, 2, 4, 8, 0, 3,... using a 74x194 shift register, a 2 Input AND gate and a 4 Input NOR gate. No other gates may be used. / Ontwerp 'n stroombaan met die volgorde 0, 3, 6, 12, 9, 2, 4, 8, 0, 3,... gebruik n 74x193 skuifregister, n 2 inset AND hek, en n 4 inset NOR hek. Geen addisionele hekke mag gebruik word nie. (18) Function Inputs Next State S1 S0 QA* QB* QC* QD* Hold 0 0 QA QB QC QD Shift right 0 1 RIN QA QB QC Shift left 1 0 QB QC QD LIN Load 1 1 A B C D ERS 220 Exam

21 2. The following figure shows a modulo-8 counter circuit. / Die volgende figuur wys 'n modulo-8 teller stroombaan. a) Complete the table below for the above counter circuit. Voltooi die onderstaande tabel vir die boonste teller stroombaan. (10) Clock Pulse QC QB QA X Y Z b) What type of sequence is generated at the output of the above counter circuit? / Watter soort volgorde is ontwikkel by die afvoer van die boonste teller stroombaan. (2) ******************* END / EINDE ******************* ERS 220 Exam

Eksamen Invulvraestel Kopiereg voorbehou. Examination Fill in paper Copyright reserved. Vakkursus ERS November 2008

Departement Elektriese, Elektroniese en Rekenaar-Ingenieurswese Department of Electrical, Electronic and Computer Engineering Eksamen Invulvraestel Kopiereg voorbehou Vakkursus ERS220 22 November 2008