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1 Code No: R Set No. 1 II B.Tech I Semester Regular Examinations, November 2007 DIGITAL LOGIC DESIGN ( Common to Computer Science & Engineering, Information Technology and Computer Science & Systems Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. (a) Perform subtraction with the following unsigned decimal numbers by taking 10 s complement of the subtrahend. Verify the result. [ ] i ii iii iv (b) Convert the given gray code number to equivalent binary [4] 2. (a) Draw the logic diagram corresponding to following expressions without simplifying them. i. (A + B) (C + D) ( A + B + D) ii. (AB + A B )(CD + C D) (b) Obtain the complement of the following Boolean expressions. [8+8] i. x yz + x yz + xy z + xy z ii. x yz + xy z + xyz + xyz iii. x z + x y + xy z + yz iv. x y?z + x yz + xy z + xy z + xyz. 3. (a) Show that A B = (A + B) + ( A + B ) and draw the circuit implementation two-level NOR-NOR form and NAND-AND form. (b) Obtain minimal POS expression for the given Boolean function f (A, B, C,D) = 0, 1, 2, 3, 4, 8, 9, 12 And draw the circuits with two?level NOR-NOR form and AND- OR form. [8+8] 4. (a) Implement 64 1 multiplexer with four 16 1 and one 4 1 multiplexer. (Use only block diagram). (b) A combinational logic circuit is defined by the following Boolean functions. F 1 = ABC + AC F 2 = ABC + AB F 3 = ABC + AB Design the circuit with a decoder and external gates. [8+8] 5. (a) Draw the circuit diagram of clocked D- flip-flop with NAND gates and explain its operation using truth table. Give its timing diagram. 1 of 2

2 Code No: R Set No. 1 (b) Explain the procedure for the design of sequential circuits with example. [8+8] 6. (a) Write the HDL structural description of the 4- bit binary counter with parallel load. (b) Design a 4-bit ring counter using D- flip flops and draw the circuit diagram and timing diagrams. [8+8] 7. Tabulate the PLA programming table for the four Boolean functions: A(x,y,z) = Σ ( 1,2,4,6) B(x,y,z) = Σ ( 0,1,6,7) C(x,y,z) = Σ ( 2,6) D(x,y,z) = Σ ( 1,2,3,5,7) Minimize the number of product terms and also show the internal logic in the PLA structure. [16] 8. (a) Give the implementation procedure for a SR Latch using NOR gates. (b) An asynchronous sequential circuit is described by the excitation and output functions. Y = x 1 x 2 + (x 1 + x 2)y Z = y Implement the circuit defined above with a NOR SR latch. Repeat with a NAND SR latch. [6+10] 2 of 2

3 Code No: R Set No. 2 II B.Tech I Semester Regular Examinations, November 2007 DIGITAL LOGIC DESIGN ( Common to Computer Science & Engineering, Information Technology and Computer Science & Systems Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. (a) Perform the following using BCD arithmetic. [4+4] i ii (b) Convert the following: i. AB 16 = ( ) 10 ii = ( ) 10 iii = ( ) 10 iv = ( ) 16 [ ] 2. (a) Simplify the following Boolean functions. i. x yz + x yz + xy z + xy z ii. x yz + xy z + xyz + xyz iii. x z + x y + xy z + yz iv. x y z + x yz + xy z + xy z + xyz. (b) Obtain the complement of the following Boolean expressions. [8+8] i. A C + ABC + AC ii. (x y + z) + z + xy + wz iii. A B(D + C D) + B(A +A CD) iv. (A + C)(A + C )(A + B + C D). 3. (a) Implement the following Boolean function F using no more than two NOR - gates and draw the circuit. F (A, B, C,D) = (0, 1, 2, 9, 11) + d (8, 10, 14, 15) (b) Implement the following Boolean function using two - level forms: [6+10] i. NAND - AND ii. AND - NOR iii. OR - NAND and iv. NOR - OR and draw the circuits. F (A, B, C,D) = Π5, 7, 9, 11, 12, 13, 14, (a) Using K-map design a combinational logic circuit to obtain 2 s complement for the given 4-bit binary number. Draw the circuit using only two input exclusive-or gates and 2- input OR gates. What is the output expression for 5 inputs? 1 of 2

4 Code No: R Set No. 2 (b) Design a combinational circuit to increment a 4-bit binary number A 3, A 2, A 1, A 0 by 1 using four half - adders. [8+8] 5. Obtain state table and state diagram for sequence recognizer to recognize the occurrence of the sequence bits 1101, and design the logic circuit. [16] 6. (a) Draw the logic diagram for a 4-bit binary ripple down counter using positive edge triggered flip-flops. (b) Write the HDL behavioral description of the 4- bit universal shift register. [8+8] 7. List the PLA programming table and draw the PLA structure for the BCD-toexcess-3-code converter. [16] 8. (a) Give the implementation procedure for a SR Latch using NOR gates. (b) An asynchronous sequential circuit is described by the excitation and output functions. Y = x 1 x 2 + (x 1 + x 2)y Z = y Implement the circuit defined above with a NOR SR latch. Repeat with a NAND SR latch. [6+10] 2 of 2

5 Code No: R Set No. 3 II B.Tech I Semester Regular Examinations, November 2007 DIGITAL LOGIC DESIGN ( Common to Computer Science & Engineering, Information Technology and Computer Science & Systems Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. Convert the following to Decimal and then to Hexadecimal. (a) (b) (c) (d) (e) (f) [ ] 2. (a) Express the following functions in sum of minterms and product of maxterms. i. F (A,B,C,D) = B D + A D + BD ii. F(x,y,z) = (xy + z)(xz + y). (b) Obtain the complement of the following Boolean expressions. [8+8] i. (AB + AC )(BC + BC )(ABC) ii. AB C + A BC + ABC iii. (ABC) (A + B + C) iv. A + B C (A + B + C ). 3. (a) Implement F = (xy + xy) (w + z) using multilevel NOR gates and draw the circuit. (b) Implement the following Boolean functions using wired - logic: [8+8] F 1 = AB CD use AOI gate F 2 = A + B C + D And draw the circuit. use AOI gate 4. (a) Implement 64 1 multiplexer with four 16 1 and one 4 1 multiplexer. (Use only block diagram). (b) A combinational logic circuit is defined by the following Boolean functions. F 1 = ABC + AC F 2 = ABC + AB F 3 = ABC + AB Design the circuit with a decoder and external gates. [8+8] 5. (a) Convert the following 1 of 2

6 Code No: R Set No. 3 i. J-K flip-flop to T- flip-flop ii. R-S flip-flop to D-flip-flop. (b) Draw the circuit diagram of positive edge triggered J-K flip-flop with NAND gates and explain its operation using truth table. How race around condition is eliminated. [8+8] 6. (a) Draw and explain 4-bit universal shift register. (b) Explain different types of shift registers. [8+8] 7. (a) Draw and explain the block diagram of PLA. (b) Tabulate the PLA programmable table for the four Boolean functions given below: A(x,y,z) = Σ m (1,2,4,6) B(x,y,z) = Σ m (0,1,6,7) C(x,y,z) = Σ m (2,6) D(x,y,z) = Σ m (1,2,3,5,7). [16] 8. (a) Give the implementation procedure for a SR Latch using NOR gates. (b) An asynchronous sequential circuit is described by the excitation and output functions. Y = x 1 x 2 + (x 1 + x 2)y Z = y Implement the circuit defined above with a NOR SR latch. Repeat with a NAND SR latch. [6+10] 2 of 2

7 Code No: R Set No. 4 II B.Tech I Semester Regular Examinations, November 2007 DIGITAL LOGIC DESIGN ( Common to Computer Science & Engineering, Information Technology and Computer Science & Systems Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. Convert the following to Binary and then to gray code. [ ] (a) (b) AB33 16 (c) (d) (e) (f) (a) Convert the following expressions in to sum of products and product of sums. i. (AB + C) ( B + C D) ii. x + x(x + y )(y + z ). (b) Obtain the Dual of the following Boolean expressions. [8+8] i. (AB + AC )(BC + BC )(ABC) ii. AB C + A BC + ABC iii. (ABC) (A + B + C) iv. A + B C (A + B + C ). 3. (a) If F 1 (A, B, C) = A B C F 2 (A, B, C) = A C B Show that = F 1 = F 2 (b) Show that A B AB = A + B (c) Obtain minimal SOP expression for the complement of the given expression: F(A, B, C) = (1, 2, 5, 7) And draw the circuit using NOR - gates. [4+4+8] 4. (a) Implement 64 1 multiplexer with four 16 1 and one 4 1 multiplexer. (Use only block diagram). (b) A combinational logic circuit is defined by the following Boolean functions. F 1 = ABC + AC F 2 = ABC + AB F 3 = ABC + AB Design the circuit with a decoder and external gates. [8+8] 1 of 2

8 Code No: R Set No (a) Draw the circuit diagram of clocked D- flip-flop with NAND gates and explain its operation using truth table. Give its timing diagram. (b) Explain the procedure for the design of sequential circuits with example. [8+8] 6. (a) Explain synchronous and ripple counters. Compare their merits and demerits. (b) Design a modulo -12 up synchronous counter using T- flip flops and draw the circuit diagram. [8+8] 7. (a) Show the memory cycle timing waveforms for the write and read operations. Assume a CPU clock of 50 MHz and a memory cycle time of 50 ns. (b) The following memory units are specified by the number of words times the number of bits per word. How many address lines and input-output data lines are needed in each case? [8+8] i. 4K * 16, ii. 2G * 8, iii. 16M * 32, iv. 256K * (a) Describe the operation of the SR Latch using NAND gate with the help of truth table, transition table and the circuit. (b) Explain the operation and use of De bounce circuit. [8+8] 2 of 2

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