Digital System Design
PART –A
- a) Given that (292)10 = (1204)b, determine b. (2M) b) List out the postulates used in Boolean algebra. (2M)
- What are the don’t care conditions of a Boolean function? (3M)
- Draw the circuit of a full adder using two half adders and OR gate. (2M)
- Convert a T flip-flop to D-type flip-flop. (3M)
- Write a note on synchronous counter. (2M)
PART –B
- a) Convert the following numbers. i) (10101100111.0101)2 to Base 10. ii) (7M)
(153.513)10 to base 8.
- b) Discuss the subtraction of two numbers using radix complement and (7M) diminished radix complement forms.
- a) Reduce the following Boolean expressions. i)AB+A(B+C)+B(B+C) (7M) ii)ABEF+ AB(EF)′+(AB)′ iii) A′B′+A′BC′+A′BCD+A′BC′D′E.
- b) Write the Postulates and theorems of Boolean Algebra. (7M)
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- Simplify the following using K-map method in SOP and POS forms. (14M)
F(A,B,C,D,E)=∑(0,2,4,6,9,11,13,15,17,21,25,27,29,31).
- a) Design a 4-bit carry look ahead adder circuit. (7M) b) Design a combinational circuit for a 2-bit magnitude comparator. (7M)
- a) Draw a neat circuit diagram of positive edge triggered D flip-flop and explain (7M) its operation.
- b) Distinguish between combinational logic and sequential logic. (7M)
- a) Explain the working of a 4-bit register which uses parallel load with a logic (7M) diagram;
- b) Design a 4-bit ripple counter using T-flip-flop. Explain using wave forms (7M)
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- a) What is the gray code equivalent of the Hexa number 3A7? (2M) b) State and prove Demorgan`s theorems. (2M)
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- a) Convert the following to required form i) (163.789)10 = ( )8 (7M)
- (101101110001.00101)2 =( )
- Perform the given subtraction using 1’s and 2’s complement methods: (7M)
(10110)2 - (1101101)2.
- a) Find the complement of the following and show that F.F′ =0 and F+ F′=1. i) (7M)
F=(x+y′+z)(x′+z′)(x+y)
- Express the following function in sum of Minterms and product of Maxterms. (7M)
- a) Obtain the simplified expression in sum of products and product of sums form (14M) using K-map method. F(A,B,C,D,E)=∑(0,1,4,5,9,16,17,21,25,29)
- a) What is a decoder? Explain a 4:16 decoder with a truth table and logic (7M) diagram.
- Write a HDL program to find the 2’s complement of an 8-bit binary number. (7M)
- a) Draw a neat circuit diagram of a negative edge triggered JK flip-flop and (7M) explain its operation.
- Explain the operation of RS master-slave flip-flop. Explain its truth table. (7M)
- a) Draw and explain 4-bit universal shift register. (7M) b) Draw the circuit diagram of 4-bit Johnson counter using D flip-flop and explain (7M) its operation with help of bit pattern.
- a) Find (72532-03250) using 9`s complement. (2M) b) Obtain the minimal sum of product expression of a given function by using (3M) consensus theorem.
- Write the properties of XOR gate. (3M)
- Write the steps involved in the design of a combinational circuit. (2M)
- Write the excitation table of a JK flipflop. (2M)
- What is a ripple counter? (2M)
PART –B
- a) Convert the following i) AB16 = ( )10 ii) 12348 = ( )10 iii) 77210 = ( )16 . (7M) b) Perform the following subtraction in binary using 1’s and 2’s complement (7M) methods: (199)10 - (254)10.
- a) What is the canonical and standard forms of a Boolean function? Explain with (7M) an example.
- Reduce the following Boolean expressions. i) ((AB)′+A′+AB)′ ii) (7M) AB+(AC)′+AB′+C(AB+C). iii)((AB′+ABC)′+A(B+AB′))′
- a) Obtain minimal POS expression for the Boolean (7M)
F(A,B,C,D)=Π(0,1,2,3,4,6,9,10)+d(7,11,13,15).draw the circuit using 2 input NAND gates.
- Prove that NAND and NOR operations are commutative but not associative. (7M)
- a) Explain 16x1 multiplexer with the help of truth table and logic diagram. (7M) b) Design a priority encoder of 4-bit. (7M)
- a) What is race around condition? Explain how is it eliminated in master-slave (7M) flip-flops with diagram?
- Convert the JK flip-flop to T flip-flop. (7M)
- a) Design a serial adder using shift register. (7M) b) Explain about the two ways to achieve a BCD counter using a counter with (7M) parallel load.
- a) Add and subtract in binary 1111 and 1010. (2M) b) Simplify the following function (x+y)(x′(y′+z′))+x′y′+x′z′. (3M)
- How the minterms, maxterms and Don’t care conditions are represented in K- (3M) map method.
- What is a priority encoder? (2M)
- Draw the circuit diagram of clocked flip-flop with NAND gates. (2M)
- Write the merits and demerits of synchronous counter. (2M)
PART –B
- a) Convert the following numbers i) (53)10 =( )2 ii) (231)4 =( )10 iii) (1101101)2 = (7M) ( )8 iv) (4D.56)16 = ( )2
- Perform the following arithmetic operation using 1’s and 2’s complement (7M) methods: (1101110)2 – (10101)2.
- a) Discuss the properties of Boolean algebra. (6M) b) Obtain the complement and dual of the following Boolean expressions. (8M)
- i) A′B+A′BC′+A′BCD+A′BC′D′ ii) ABEF+ABE′F′+A′B′EF
- a) If F1(A,B,C,D)=∑(1,3,4,5,9,10,11)+d(6,8) and (7M)
F2(A,B,C,D)=∑(0,2,4,7,8,15)+d(9,12) . Obtain minimal SOP expression for F1⊕ F2 using k-map and draw the circuit using NAND gates.
- Draw NOR logic diagram that implements the following function. (7M)
F(A,B,C,D)=Π(0,1,2,3,4,8,9,12)
- a) Draw the circuit diagram of a full subtractor using NOR gates. (7M) b) What is decoder? Construct a 4:16 decoder with two 3:8 decoders. (7M)
- a) Design a finite state machine which can detect the sequence 0010 by using JK (7M) flip-flop.
- Discuss in detail about sequential circuits with examples. (7M)
- a) Explain universal shift registers with truth tables. (7M) b) Design a Mod-10 counter with T flip-flops. (7M)
- a) (22B)x =(555)10 then Find the value of ‘x’ (2M) b) Simplify the following Boolean functions (i) X (Xl +Y) (ii) XY+YZ +XlZ (3M)
- c) Write the Max terms corresponding to the logical expression (2M)
Y = (A+B+Cl). (A+Bl+Cl).(Al+Bl+C)
- Implement XOR gate by using NAND gates. (2M)
- Write the excitation table for T Flip-flop. (3M)
- Define synchronous counter. (2M)
PART -B
- a) How do you convert a gray number to binary? Generate a 4-bit gray code (8M) directly using the mirror image property?
- Write the comparison between 1’s complement and 2’s complement. (6M)
- a) Simplify the following (7M)
(i)AB+ BC+ AlC = AB+ AlC (ii) (X+Y).(Yl+Z) = X
- Convert the following expression into SOP and POS (7M)
(i) (AB+C)(B+ ̅ ) (ii) ̅+(x+ )(y+ ̅)
- a) Simplify the following function using K-Map f(a,b,c,d)= ∑m(3,7,11,12,13,14,15)
- Design an odd parity circuit using XOR gate.
- a) Draw and explain the 8×1 MUX. (7M) b) Convert the BCD to XS-3 and XS-3 to BCD by using a full adder. (7M)
- a) What is Race condition and explain about the operation of clocked RS flip- (7M) flop.
- Convert the JK Flip-flop into RS flip-flop. (7M)
- a) Design a 4-bit ring counter with as in table figure. (7M) b) Design a 4 bit shift left register using flip flops. (7M)