# UNIT I BOOLEAN ALGEBRA AND COMBINATIONAL CIRCUITS PART-A (2 MARKS)

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1 SUBJECT NAME: DIGITAL LOGIC CIRCUITS YEAR / SEM : II / III DEPARTMENT : EEE UNIT I BOOLEAN ALGEBRA AND COMBINATIONAL CIRCUITS 1. What is variable mapping? 2. Name the two canonical forms for Boolean algebra. 3. State the steps involved in Gray to binary conversion? 4. State De Morgan's theorem. 5. Reduce A'B'C' + A'BC' + A'BC 6. Prove that ABC + ABC' + AB'C + A'BC = AB + AC + BC 7. State the limitations of karnaugh map. 8. What is a full-adder? 9. What is Magnitude Comparator? 10.What is code conversion? 11.Give an application each for a mux and demux. 12.What is a priority encoder? 13. Implement the given function in 4:1 mux f= Σm(0,1,3,5,6) 14. Can a decoder function as a Demultiplexer? 15.What are prime-implicants?

2 1. Obtain the minimum sop using QUINE- McCLUSKY method and verify using K-map F=m0+m2+m4+m8+m9+m10+m11+m12+m13 (16) 2. Reduce the following using tabulation method. (16) F=m2+m3+m4+m6+m7+m9+m11+m13. 3.Reduce the Boolean function using k-map technique and implement using gates f (w, x, y, z)= Σm (0,1,4,8,9,10) which has the don t cares condition d (w, x, y, z)= Σm (2,11). (16) 4. a) Design an 8421 to gray code converter. (8) b) Implement the Boolean function using 8:1 mux. (8) F (A, B, C, D) =A BD +ACD+B CD+A C D. 5. Design A Full Adder And A Full Subtractor. (16) 6 A combinational circuit is defined by the following three Boolean functions F1 = x y z +xz F2= xy z +x y F3= x y z+xy Design the circuit with a decoder and external gates. (16) 7. Simplify the following Boolean function by using Tabulation method F (w, x, y, z) = m (0, 1, 2, 8, 10, 11, 14, 15) (16) 8. Simplify the following Boolean functions by using K Map in SOP & POS. F (w, x, y, z) = m (1, 3, 4, 6, 9, 11, 12, 14) (16) 9. a) Design a 2 bit magnitude comparator. (8) b) Explain the operation of 4 to 10 decoder. (8)

3 SYNCHRONOUS SEQUENTIAL SIRCUITS 1. Write the characteristic equations for Jk and D Flip Flops. 2. How can a D flip flop be converted into T flip-flop? 3. What is meant by the term edge triggered? 4. How many ff s are required to design a mod-7 up down counter? 5. Define synchronous sequential circuit 6. Define flip flop 7. What is race around condition? 8. What is the difference between synchronous and asynchronous counter? 9. What is meant by modulus of a counter? 10. What is a state equation? (i) (ii) PART B 1. A sequential circuit has 2D ff s A and B an input x and output y is specified by the following next state and output equations. A (t+1)= Ax + Bx B (t+1)= A x Y= (A+B) x Draw the logic diagram of the circuit. Derive the state table. (iii) Derive the state diagram. (16) 2. Design a mod-10 synchronous counter using Jk ff. write excitation table and state table. (16) 3. a)write the excitation tables of SR, JK, D, and T Flip flops (8) b) Realize D and T flip flops using Jk flip flops (8)

4 (16) 5. Design a counter with the following repeated binary sequence:0, 1, 2, 3, 4, 5, 6.use JK Flip-flop. (16) UNIT III ASYNCHRONOUS SEQUENTIAL CIRCUIT 1. Distinguish between synchronous and asynchronous sequential circuits 2. What is an essential hazard and how to eliminate it? 3. What is meant by state assignment? 4. Define Asynchronous sequential circuit? 5. What is the significance of state assignment? 6. What is primitive flow chart? 7. What is fundamental mode? 8. What are the steps for the design of asynchronous sequential circuit? 9. Define merger graph. 10. When do race conditions occur?

5 PART B 1. Design an asynchronous sequential circuit that has 2 inputs x2 and x1, and one output z. the output is to remain 0 as long as an X1 is 0. The first change in x2 that occurs while x1 is 1 will cause z to be 1. Z is to remain 1 until x1 returns to 0. Construct a state diagram and flow table. Determine the output equations. (16) 2.Design a circuit with inputs A and B to give an output z=1 when AB=11 but only if A becomes 1 before B, by drawing total state diagram, primitive flow table and output map in which transient state is included. (16) 3. Obtain the primitive flow table for an asynchronous circuit that has 2 input s x, y and output z. an output z=1, is to occur only during the input state xy=01 and then if and only if the input state xy=01 is preceded by the input sequence xy=01, 00, 10, 00, 10, 00 (16) 4. Design a circuit with input a and b to give an output z=1 when AB =11 but only if A becomes 1 before B, by drawing total state diagram, primitive flow table and output map in which transient state is included. (16) 5. Design a asynchronous sequential circuit with 2 inputs T and C. The output attains a value of 1 when T = 1 & c moves from 1 to 0. Otherwise the output is 0. (16) 6. Design an Asynchronous sequential circuit using SR latch with two inputs A and B and one output y. B is the control input which, when equal to 1, transfers the input A to output y. when B is 0, the output does not change, for any change in input. (16)

6 PROGRAMMABLE LOGIC DEVICS,MEMORY AND LOGIC FAMILIES 1. Mention the classification of saturated bipolar logic families 2. What are the difference between PLA and PAL? 3. What is the major difference between ECL and TTL? 4. What are the types of TTL logic? 5. Define address and word: 6. What is programmable logic array? How it differs from ROM? 7. Explain EPROM. 8. Give the classification of PLD s. 9. Define Static RAM and dynamic RAM PART B 1. a) Explain in detail about PLA with a specific example. (8) b) Explain with neat diagrams RAM architecture (8) 2. Implement the following function using PLA. A (x, y, z) = m (1, 2, 4, 6) B (x, y, z) = m (0, 1, 6, 7) C (x, y, z) = m (2, 6) (16) 3. Implement the following function using PAL. W (A, B, C, D) = m (2, 12, 13) X (A, B, C, D) = m (7, 8, 9, 10, 11, 12, 13, 14, 15) Y (A, B, C, D) = m (0, 2, 3, 4, 5, 6, 7, 8, 10, 11, 15) Z (A, B, C, D) = m (1, 2, 8, 12, 13) (16)

7 VHDL 1) What do the acronyms VHDL and VHLSI stand for? 2) What are the advantages of using a hard ware description language? 3) What is VHDL? 4) What are the features of VHDL 5) Define entity 6) What do you meant by concurrent statement 7) Define VHDL package 8) What are the operates used in VHDL language 9) Give short notes on logic simulation and logic synthesis 10)What do you mean by test bench

8 PART B 1) Write a HDL code for state machine to BCD to ex 3 codes Converter (16) 2) Write a behavioral VHDL description of the 4 bit counter (16) 3) (I) Write VHDL code for a full sub tractor using logic Equation (8) (II) Write a VHDL description of an S-R latch using a process (8) 4) Write a HDL code for 8:1 MUX using behavioral model (16) 5) Write the HDL description of the circuit specified by the Following Boolean equations (16) S = xy + x y C =xy 6) (I) Write an HDL data flow description of a 4 bit adder subtractor of Unsigned numbers use the conditional operator (8) (II) Write the HDL gate level description of the priority encoder (8) *****************************************

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