EC-303 Digital System Design - Dec 2024 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 14 Marks
   Convert the following:

   1. a)$(4097.188)_{10} = (\quad)_{2}$
   2. b)$(011.101101)_{2} = (\quad)_{8}$
   3. c)$(2645)_{8} = (\quad)_{2}$
   4. d)$(381B)_{16} = (\quad)_{8}$
   5. e)$(457)_{10} = (\quad)_{gray}$
   How to answer

   • Recall base conversion methods for integer and fractional parts
   • Convert each given number step by step to target base
   • Show intermediate binary/octal/hex groupings
   • Write final result in required base including Gray conversion logic
2. 7 Marks
   aSimplify the following function: $Y = \bar{A}B + ABD + \bar{A}BC\bar{D} + BC$ $Y = A + \bar{A}B + \bar{A}\bar{B}C + \bar{A}\bar{B}\bar{C}D$
   How to answer

   • State Boolean laws used (absorption, distributive, complement)
   • Simplify first expression $Y = \bar{A}B + ABD + \bar{A}B\bar{C}\bar{D} + BC$ step by step
   • Simplify second expression $Y = A + \bar{A}B + \bar{A}\bar{B}C + \bar{A}\bar{B}\bar{C}D$ step by step
   • Write final minimized sum-of-products form
3. 7 Marks
   bSimplify the following function using K-map. $Y = \bar{A}BC + CD + AC\bar{D}$ $Y = \sum_{m}(0,1,6,7) + \sum_{d}(8,9,10,11,12)$
   How to answer

   • Plot 4-variable K-map for given minterms and don't cares
   • Form maximal groups of 1s using don't cares where helpful
   • Derive prime implicants and essential prime implicants
   • Write final minimized expression for Y
4. 14 Marks
   Minimize the following function using Quine McCluskey method. $f = \Sigma(1, 2, 3, 7, 8, 9, 10, 11, 14, 15)$
   How to answer

   • List minterms in binary and group by number of 1s
   • Perform successive tabular combination to find prime implicants
   • Construct prime implicant chart and find essential prime implicants
   • Write minimal cover expression for f
5. 7 Marks
   aDesign a full adder using two half adders.
   How to answer

   • Recall half-adder equations for Sum and Carry
   • Combine two half-adders with inputs A, B, Cin
   • Add OR gate for final carry $Cout = C1 + C2$
   • Draw block diagram and give truth table
6. 7 Marks
   bDesign a BCD adder.
   How to answer

   • Explain need for correction when sum > 9 in BCD
   • Use two 4-bit binary adders and correction logic
   • Derive correction condition $C + S3S2 + S3S1$
   • Draw block diagram adding 0110 when correction needed
7. 7 Marks
   aWith the help of circuit diagram explain the working of J-K flip-flop. Also explain race around condition.
   How to answer

   • Draw NAND-based J-K flip-flop circuit diagram
   • Explain J,K = 00,01,10,11 operations with truth table
   • Define race-around condition when J=K=1 with long clock
   • Mention master-slave solution to avoid racing
8. 7 Marks
   bDesign a Pseudo Random Binary sequence generator.
   How to answer

   • Define PRBS and use of LFSR with XOR feedback
   • Select shift-register length and feedback polynomial
   • Draw LFSR circuit diagram for maximal length sequence
   • Explain pseudo-random output sequence generation
9. 14 Marks
   Design a MOD-6 counter using J-K flip flop.
   How to answer

   • Determine 3 flip-flops needed for 6 states (000 to 101)
   • Draw state diagram and excitation table for J-K inputs
   • Derive minimized J,K expressions using K-maps
   • Draw logic diagram with reset on 110 and explain counting sequence
10. 14 Marks
    Explain the following logic families.

    1. a)Tri state TTL
    2. b)CMOS
    How to answer

    • Define logic family characteristics to compare
    • Explain Tri-state TTL operation with high, low, high-impedance states
    • Explain CMOS inverter structure with PMOS-NMOS pair and advantages
    • Give circuit diagrams and applications
11. 14 Marks
    Write short notes on any two of the following:

    1. a)Binary Multiplier and Binary Divider
    2. b)Parity checker
    3. c)FPGA
    How to answer

    • Select any two topics with definition and block diagram
    • Explain principle of operation and key equations/logic
    • Mention advantages, limitations and applications
    • Conclude with neat labelled diagram