Anna University, Chennai

**M****.****A****.****M SCHOOL OF ENGINEERING**

**S****I****RUGANUR, TRICHY**

**D****E****P****AR****T****M****E****N****T ****O****F ELECTRONICS & COMMUNICATION ENGINEERING**

**CS2202 DIGITAL PRINCIPLES AND SYSTEM DESIGN**

**B****r****anch/Sem ****: ECE / III**

**Unit – I Boolean algebra and Logic Gates**

**P****art A**

**1. Find the hexadecimal equivalent of the decimal number 256**

**2. Find the octal equivalent of the decimal number 64**

**3. What is meant by weighted and non-weighted coding?**

**4. Convert A3BH and 2F3H into binary and octal respectively**

**5. Find the decimal equivalent of (123)****9**

**6. Find the octal equivalent of the hexadecimal number AB.CD**

**7. Encode the ten decimal digits in the 2 out of 5 code**

**8. Show that the Excess – 3 code is self –complementing**

**9. Find the hexadecimal equivalent of the octal number 153.4**

**10. Find the decimal equivalent of (346)****7**

**11. A hexadecimal counter capable of counting up to at least (10,000)****1****0 ****i****s to be constructed. What is the minimum number of hexadecimal digits that the counter must have?**

**12. Convert the decimal number 214 to hexadecimal**

**13. Convert 231.3 ****4 ****to base 7**

**14. Give an example of a switching function that contains only cyclic prime implicant**

**15. Give an example of a switching function that for which the MSP from is not unique.**

**16. Express x+yz as the sum of minterms**

**17. What is prime implicant?**

**18. Find the value of X = A B C (A+D) if A=0; B=1; C=1 and D=1**

**19. What are ‘minterms’ and ‘maxterms’?**

**20. State and prove Demorgan’s theorem**

**21. Find the complement of x+yz**

**22. Define the following : minterm and term**

**23. State and prove Consensus theorem**

**24. What theorem is used when two terms in adjacent squares of K map are combined?**

**25. How will you use a 4 input NAND gate as a 2 input NAND gate?**

**26. How will you use a 4 input NOR gate as a 2 input NOR gate?**

**27. Show that the NAND connection is not associative**

**28. What happens when all the gates is a two level AND-OR gate network are replaced by**

**N****O****R gates?**

**29. What is meant by multilevel gates networks?**

**30. Show that the NAND gate is a universal building block**

**31. Show that a positive logic NAND gate is the same as a negative logic NOT gate**

**32. Distinguish between positive logic and negative logic**

**33. Implement AND gate and OR gate using NAND gate**

**34. What is the exact number of bytes in a system that contains (a) 32K byte, (b) 64M bytes, and (c) 6.4G byte?**

**35. List the truth table of the function: F = x y + x y’ + y ’z**

**P****art B**

**1. (a) Explain how you will construct an (n+1) bit Gray code from an n bit**

**Gr****ay code**

**(b) Show that the Excess – 3 code is self -complementing**

**2. (a) Prove that (x1+x2).(x1’. x3’+x3) (x2’ + x1.x3) =x1’x2**

**(b) Simplify using K-map to obtain a minimum POS expression:**

**(A’ + B’+C+D) (A+B’+C+D) (A+B+C+D’) (A+B+C’+D’) (A’+B+C’+D’) (A+B+C’+D)**

**3. Reduce the following equation using Quine McClucky method of**

**m****i****n****i****m****iz****ation F (A,B,C,D) = _m(0,1,3,4,5,7,10,13,14,15)**

**4. (a) State and Prove idempotent laws of Boolean algebra.**

**(b) using a K-Map ,Find the MSP from of F= _(0,4,8,12,3,7,11,15) +_d(5)**

**5 (a) With the help of a suitable example ,explain the meaning of an redundant prime i implicant**

**(b) Using a K-Map, Find the MSP form of F= _ (0-3, 12-15) + _d (7, 11)**

**6 (a) Simplify the following using the Quine – McClusky minimization technique D = f(a,b,c,d) = _ (0,1,2,3,6,7,8,9,14,15).Does Quine –McClusky take care of don’t care conditions? In the above problem, will you consider any don’t care conditions? Justify your answer**

**(b) List also the prime implicants and essential prime implicants for the above case**

**7 (a) Determine the MSP and MPS focus of F= _ (0, 2, 6, 8, 10, 12, 14, 15)**

**(b) State and Prove Demorgan’s theorem**

**8 Determine the MSP form of the Switching function**

**F = _ ( 0,1,4,5,6,11,14,15,16,17,20- 22,30,32,33,36,37,48,49,52,53,56,63)**

**9. (a) Determine the MSP form of the Switching function**

**F****( a,b,c,d) =_(0,2,4,6,8) + _d(10,11,12,13,14,15)**

**(b) Find the Minterm expansion of f(a,b,c,d) = a’(b’+d) + acd’**

**10 Simplify the following Boolean function by using the Tabulation Method**

**F****= _ (0, 1, 2, 8, 10, 11, 14, 15)**

**11 State and Prove the postulates of Boolean algebra**

**12 (a) Find a Min SOP and Min POS for f = b’c’d + bcd + acd’ + a’b’c + a’bc’d**

**13 Find an expression for the following function usingQuine McCluscky method**

**F****= _ (0, 2, 3,5,7,9,11,13,14,16,18,24,26,28,30)**

**14 State and Prove the theorems of Boolean algebra with illustration**

**15 Find the MSP representation for**

**F****(A,B,C,D,E) = _m(1,4,6,10,20,22,24,26) + _d (0,11,16,27) using K-Map method**

**D****r****aw the circuit of the minimal expression using only NAND gates**

**16 (a) Show that if all the gates in a two – level AND-OR gate networks are replaced by**

**NAN****D gates the output function does not change**

**(b) Why does a good logic designer minimize the use of NOT gates?**

**17 Simplify the Boolean function F(A,B,C,D) = _ m (1,3,7,11,15) + _d (0,2,5) .if don’t care conditions are not taken care, What is the simplified Boolean function .What are your comments on it? Implement both circuits**

**18 (a) Show that if all the gate in a two – level OR-AND gate network are replaced by NOR**

**gate, the output function does not change.**

**(b) Implement Y = (A+C) (A+D’) ( A+B+C’) using NOR gates only**

**19 (a) F3 = f(a,b,c,d) = _ (2,4,5,6) F2 = f(a,b,c,d) = _ (2,3,,6,7)**

**F****1 = f(a,b,c,d) = _ (2,5,6,7) .Implement the above Boolean functions**

**(i) When each is treated separately and**

**(ii)When sharing common term**

**(b) Convert a NOR with an equivalent AND gate**

**20 Implement the Switching function whose octal designation is 274 using NAND gates only**

**21 Implement the Switching function whose octal designation is 274 using NOR gates only**

**22 (a) Show that the NAND operation is not distributive over the AND operation**

**(b) Find a network of AND and OR gate to realize f(a,b,c,d) = _ m (1,5,6,10,13,14)**

**23 What is the advantages of using tabulation method? Determine the prime implicants of the following function using tabulation method**

**F****( W,X,Y,Z) = _(1,4,6,7,8,9,10,11,15)**

**23 (a) Explain about common postulates used to formulates various algebraic structures**

**(b) Given the following Boolean function F= A”C + A’B + AB’C + BC Express it in sum of minterms & Find the minimal SOP expression ****Unit – II Combinational Logic**

**P****art A**

**1. How will you build a full adder using 2 half adders and an OR gate?**

**2. Implement the switching function Y= BC’ + A’B + D**

**3. Draw 4 bit binary parallel adder**

**4. Write down the truth table of a full adder**

**5. Write down the truth table of a full sub tractor**

**6. Write down the truth table of a half sub tractor**

**7. Find the syntax errors in the following declarations (note that names for primitive gates are optional):**

**module Exmp1-3(A, B, C, D, F)**

**i****np****u****ts A,B,C,**

**and g1(A,B,D); not (D,B,A); OR (F,B,C); endmodule ;**

**8. Draw the logic diagram of the digital circuit specified by module circt (A,B,C,D,F);**

**i****np****u****t A,B,C,D;**

**output F;**

**w****ir****e w,x,y,z,a,d; and (x,B,C,d); and y,a,C);**

**and (w,z,B);**

**o****r (z,y,A); or (F,x,w); not (a,A); not (d,D); endmodule**

**9. Define Combinational circuits**

**10. Define Half and Full adder**

**11. Give the four elementary operations for addition and subtraction**

**12. Design the combinational circuit with 3 inputs and 1 output. The output is 1 when the binary value of the inputs is less than 3.The output is 0 otherwise**

**13. Define HDL**

**14. What do you mean by carry propagation delay?**

**15. What is code converter?**

**16. Give short notes on Logic simulation and Logic synthesis**

**17. What do you mean by functional and timing simulation?**

**18. What do you mean by test bench?**

**19. Give short notes on simulation versus synthesis**

**20. Define half sub tractor and full sub tractor**

**P****art B**

**1 Design a 4 bit magnitude comparator to compare two 4 bit number**

**2 Construct a combinational circuit to convert given binary coded decimal number into an Excess 3 code for example when the input to the gate is 0110 then the circuit should generate output as 1001**

**3 Design a combinational logic circuit whose outputs are F1 = a’bc + ab’c and**

**F****2 = a’ + b’c + bc’**

**4 (a) Draw the logic diagram of a *-bit 7483 adder**

**(b) Using a single 7483, Draw the logic diagram of a 4 bit adder/sub tractor**

**5 (a) Draw a diode ROM, which translates from BCD 8421 to Excess 3 code**

**(b) Distinguish between Boolean addition and Binary addition**

**6 Realize a BCD to Excess 3 code conversion circuit starting from its truth table**

**7 (a) Design a full sub tractor**

**(b) How to it differ from a full sub tractor**

**8 Design a combinational circuit which accepts 3 bit binary number and converts its equivalent excess 3 codes**

**9 Derive the simplest possible expression for driving segment “a” through ‘g’ in an 8421**

**B****C****D to seven segment decoder for decimal digits 0 through 9 .Output should be active high (Decimal 6 should be displayed as 6 and decimal 9 as 9)**

**10 Write the HDL description of the circuit specified by the following Boolean function**

**(i) Y= (A+B+C) (A’+B’+C’)**

**(ii) F= (AB’ + A’B) (CD’+C’D) (iii) Z = ABC + AB’ + A(D+B) (iv) T= [(A+B} {B’+C’+D’)]**

**11 Design 16 bit adder using 4 7483 ICs ****Unit – III Design with MSI Devices ****P****art A**

**1. What is a decoder and obtain the relation between the number of inputs ‘n’ and outputs**

**‘m’ of a decoder?**

**2. Distinguish between a decoder and a demultiplexer**

**3. Using a single IC 7485 ; draw the logic diagram of a 4 bit comparator**

**4. what is decoder**

**5. What do you mean by encoder?**

**6. Write the short notes on priority encoder**

**7. What is multiplexer? Draw the logic diagram of8 to 1 line multiplexer**

**8. What do you mean by comparator?**

**9. Write the HDL description of the circuit specified by the following Boolean function**

**X****=AB+ACD+BC’**

**10. How does ROM retain information?**

**11. Distinguish between PAL and PLA**

**12. Give the classification of memory**

**13. What is refreshing? How it is done?**

**14. What is Hamming code?**

**15. Write a short notes on memory decoding**

**16. List the basic types of programmable logic devices**

**17. What is PAL? How it differ from PROM and PLA?**

**18. Write a short notes on – PROM,EPROM,EEPROM**

**19. How many parity bits are required to form Hamming code if massage bits are 6?**

**20. How to find the location of parity bits in the Hamming code?**

**21. Generate the even parity Hamming codes for the following binary data**

**1101, 1001**

**22. A seven bit Hamming code is received as 11111101. What is the correct code?**

**23. Compare static RAMs and dynamic RAMs**

**24. Define Priority encoder**

**25. Define PLDs**

**P****art B**

**1. Implement the switching function F= _(0,1,3,4,7) using a 4 input MUX and explain**

**2. Explain how will build a 64 input MUX using nine 8 input MUXs**

**3. State the advantages of complex MSI devices over SSI gates**

**4. Implement the switching function F(A,B,C) = _ ( ,2,4,5) using the DEMUX 74156**

**5. Implement the switching function F= _(0,1,3,4,12,14,15) using an 8 input MUX**

**6. Explain how will build a 16 input MUX using only 4 input MUXs**

**7. Explain the operation of 4 to 10 line decoder with necessary logic diagram**

**8. Draw a neat sketch showing implementation of Z1 = ab’d’e + a’b’c’e’ + bc + de ,**

**Z2 = a’c’e, Z3 = bc +de+c’d’e’+bd and Z4 = a’c’e +ce using a 5*8*4 PLA**

**9. Implement the switching functions: Z1 = ab’d’e + a’b’c’e’ + bc + de ,**

**Z2 = a’c’e,**

**Z3 = bc +de+c’d’e’+bd and**

**Z4 = a’c’e +ce Using a 5*8*4 PLA**

**10 Design a switching circuit that converts a 4 bit binary code into a 4 bit Gray code using**

**R****O****M array**

**11.Design a combinational circuit using a ROM ,that accepts a 3- bit number and generates an output binary number equal to the square of the given input number ****Unit – IV Synchronous Sequential Logic**

**P****art A**

**1. Derive the characteristic equation of a D flip flop**

**2. Distinguish between combinational and sequential logic circuits**

**3. What are the various types of triggering of flip-flops?**

**4. Derive the characteristic equation of a T flip flop**

**5. Derive the characteristic equation of a SR flip flop**

**6. What is race round condition? How it is avoided?**

**7. List the functions of asynchronous inputs**

**8. Define Master slave flip flop**

**9. Draw the state diagram of ‘T’ FF, ‘D’ FF**

**10. Define Counter**

**11. What is the primary disadvantage of an asynchronous counter?**

**12. How synchronous counters differ from asynchronous counters?**

**13. Write a short note on counter applications**

**14. Compare Moore and Mealy models**

**15. When is a counter said to suffer from lock out?**

**16. What is the minimum number of flip flops needed to build a counter of modulus z 8?**

**17. State the relative merits of series and parallel counters**

**18. What are Mealy and Moore machines?**

**19. When is a counter said to suffer from lockout?**

**20. What is the difference between a Mealy machine and a Moore Machines?**

**21. Distinguish between synchronous and asynchronous sequential logic circuits**

**22. Derive the characteristic equation of a JK flip flop**

**23. How will you convert a JK flip flop into a D flip flop**

**24. What is mean by the term ‘edge triggered’?**

**25. What are the principle differences between synchronous and asynchronous networks**

**26. What is lockout? How it is avoided?**

**27. What is the pulse mode operation of asynchronous sequential logic circuits not very**

**p****o****p****u****l****ar?**

**28. What are the advantages of shift registers?**

**29. What are the applications of a shift register?**

**30. How many flip –flops are needed to build an 8 bit shift register?**

**31. A shift register comprises of JK flip-flops. How will you complement of the counters of the register**

**32. List the basic types of shift registers in terms of data movement.**

**33. Write a short notes on PRBS generator**

**34. Give the HDL dataflow description for T flip - flop**

**35. Give the HDL dataflow description for JK flip – flop**

**P****art B**

**1 Draw the state diagram and characteristics equation of T FF, D FF and JK FF**

**2 (a) What is race around condition? How is it avoided?**

**(b) Draw the schematic diagram of Master slave JK FF and input and output waveforms.Discuss how it prevents race around condition**

**3 Explain the operation of JK and clocked JK flip-flops with suitable diagrams**

**4 Draw the state diagram of a JK flip- flop and D flip – flop**

**5 Design and explain the working of a synchronous mod – 3 counter**

**6 Design and explain the working of a synchronous mod – 7 counter**

**7 Design a synchronous counter with states 0,1, 2,3,0,1 …………. Using JK FF**

**8 Using SR flip flops, design a parallel counter which counts in the sequence**

**000,111,101,110,001,010,000 ………….**

**9 Using JK flip flops, design a parallel counter which counts in the sequence**

**000,111,101,110,001,010,000 ………….**

**10 (a) Discuss a decade counter and its working principle**

**(b) Draw as asynchronous 4 bit up-down counter and explain its working**

**11 (a) How is the design of combinational and sequential logic circuits possible with PLA? (b) Mention the two models in a sequential circuit and distinguish between them**

**12 Design a modulo 5 synchronous counter using JK FF and implement it. Construct its timing diagram**

**12 A sequential machine has one input line where 0’s and 1’s are being incident. The machine has to produce a output of 1 only when exactly two 0’s are followed by a ‘1’ or exactly two 1’s are followed by a ‘0’.Using any state assignment and JK flipflop,synthesize the machine**

**13 Using D flip –flop ,design a synchronous counter which counts in the sequence**

**000, 001, 010, 011, 100, 1001,110,111,000**

**15 Using JK flip-flops, design a synchronous sequential circuit having one and one output. the output of the circuit is a 1 whenever three consecutive 1’s are**

**o****bs****er****v****e****d****. Otherwise the output is zero**

**14 Design a binary counter using T flip – flops to count in the following sequences: (i) 000,001,010,011,100,101,110,111,000**

**(ii) 000,100,111,010,011,000**

**15 (a) Design a synchronous binary counter using T flip – flops**

**(b) Derive the state table of a serial binary adder**

**17. Design a 3 bit binary Up-Down counter**

**18. (i) Summarize the design procedure for synchronous sequential circuit**

**(ii) Reduce the following state diagram**

**Unit – V Asynchronous Sequential Logic**

**P****art A**

**1. Distinguish between fundamental mode and pulse mode operation of asynchronous sequential circuits**

**2. What is meant by Race?**

**3. What is meant by critical race?**

**4. What is meant by race condition in digital circuit?**

**5. Define the critical rate and non critical rate**

**6. What are races and cycles?**

**7. What is the significance of state assignment?**

**8. What are the steps for the analysis of asynchronous sequential circuit?**

**9. What are the steps for the design of asynchronous sequential circuit?**

**10. Write short notes on (a) Shared row state assignment**

**(b) One hot state assignment**

**11. What are Hazards?**

**12. What is a static 1 hazard?**

**13. What is a static 0 hazard?**

**14. What is dynamic hazard?**

**15. Define static 1 hazard, static 0 hazards, and dynamic hazard?**

**16. Describe how to detect and eliminate hazards from an asynchronous network?**

**17. What is static hazard?**

**18. List the types of hazards?**

**19. How to eliminate the hazard?**

**20. Draw the wave forms showing static 1 hazard?**

**P****art B**

**1. What is the objective of state assignment in asynchronous circuit? Give hazard – free realization for the following Boolean function f(A,B,C,D) = _M(0,2,6,7,8,10,12)**

**2. Summarize the design procedure for asynchronous sequential circuit a. Discuss on Hazards and races**

**b****. What do you know on hardware descriptive languages?**

**3. Design an asynchronous sequential circuit with 2 inputs X and Y and with one output Z Wherever Y is 1, input X is transferred to Z .When Y is 0; the output does not change for any change in X.Use SR latch for implementation of the circuit**

**4. Develop the state diagram and primitive flow table for a logic system that has 2 inputs,x and y and an output z.And reduce primitive flow table. The behavior of the circuit is stated as follows. Initially x=y=0. Whenever x=1 and y = 0 then z=1, whenever x = 0 and y = 1**

**then z = 0.When x=y=0 or x=y=1 no change in z ot remains in the previous state. The logic system has edge triggered inputs with out having a clock .the logic system changes state on the rising edges of the 2 inputs. Static input values are not to have any effect in changing the Z output**

**5. Design an asynchronous sequential circuit with two inputs X and Y and with one output Z. Whenever Y is 1, input X is transferred to Z.When Y is 0,the output does not change for**

**any change in X.**

**6. Obtain the primitive flow table for an asynchronous circuit that has two inputs x,y and one output Z. An output z =1 is to occur only during the input state xy = 01 and then if the only if the input state xy =01 is preceded by the input sequence.**

**7. A pulse mode asynchronous machine has two inputs. It produces an output whenever two consecutive pulses occur on one input line only .The output remains at ‘1’ until a pulse has occurred on the other input line. Draw the state table for the machine.**

**8.**

**(a) How will you minimize the number of rows in the primitive state table of an incompletely specified sequential machine**

**(b) State the restrictions on the pulse width in a pulse mode asynchronous sequential machine**

**9. Construct the state diagram and primitive flow table for an asynchronous network that has two inputs and one output. The input sequence X1X2 = 00,01,11 causes the output to**

**b****ec****om****e 1.The next input change then causes the output to return to 0.No other inputs will produce a 1 output**