## Digital Principles and System Design - May 2014

### First Year Engineering (Semester 2)

TOTAL MARKS:

TOTAL TIME: HOURS

**1** Find the octal equivalent of hexadecimal numbers AB.CD(2 marks)
**10** Define ASIC.(2 marks)

### Answer any one question from Q11 (a) & Q11 (b)

**11 (a)** Simplify the following functions, using K-map techniques

(i) G=Π_{M}(0, 1, 3, 7, 9, 11)

(ii) f(W,X,Y,Z)=Σm(0, 7, 8, 9, 10, 12)+ Σd(2, 5, 13)(16 marks)
**11 (b)** Minimize the expression using Quine McCluskey (Tabulation) method F=Σm (0,1,9,15,24,29,30)+Σd(8,11,31)(16 marks)

### Answer any one question from Q12 (a) & Q12 (b)

**12 (a)** Design a circuit that converts 8421 BCD code to Excess-3 code.(16 marks)
**12 (b)** Implement the following Boolean function using 8 to 1. Multiplexer F(A, B, C, D)= A'BD'+ACD+B'CD+A'C'D. Also implement the function using 16 to 1 multiplexer.(16 marks)

### Answer any one question from Q13 (a) & Q13 (b)

**13 (a)** Implement T flip flop using D flip flop and JK flip flop using D flip flop.(16 marks)
**13 (b)** Design a synchronous conunter which counts in the sequence 000, 001, 010, 011, 100, 101, 111, 000 using D-FF.(16 marks)

### Answer any one question from Q14 (a) & Q14 (b)

**14 (a)** Explain the steps for the design of asynchronous sequential circuits.(16 marks)
**14 (b)** Implement the switching function F=?m(1,3,5,7,8,9,14,15) by a static hazard free two level AND OR gate network.(16 marks)
**15 (a)** Implement the following function using PLA

A(x,y,z)=Σm(1,2,4,6)

B(x,y,z)=Σm(0,1,6,7)

C(x,y,z)=Σm(2,6)(16 marks)
**15 (b)** The following messages have been coded in the even parity Hamming code and transmitted through a noisy channel. Decode the messages, assuming that at most a single error has occurred in each codeword.

(i) 1001001

(ii) 0111001

(iii) 1110110

(iv) 0011011.(16 marks)
**2** State and prove the consensus theorem.(2 marks)
**3** Implement the function G=Σm(0,3) using a 2×4 decoder.(2 marks)
**4** Draw the circuit for 2-to-1 line multuplexer.(2 marks)
**5** Write the characteristics table and equation of JK flip flop.(2 marks)
**6** Write any two applications of shift register.(2 marks)
**7** Define Race condition.(2 marks)
**8** What are the types of hazards?(2 marks)
**9** What is memory decoding?(2 marks)