CS-304 Digital Systems / Digital Circuits and System - 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. 7 Marks
   aConvert the following decimal numbers to the indicated bases:

   1. i)$(516)_7 = ()_{10} = ()_{16}$
   2. ii)$(250.5)_{10} = ()_8 = ()_4$
   3. iii)$(2ED)_{16} = ()_8 = ()_2$
   4. iv)Obtain the 9's and 10's complement of $(864)_{10}$.
   How to answer

   • Convert base-7 to decimal by positional weights then decimal to hex by repeated division
   • Convert decimal fraction to octal and base-4 by repeated multiplication/division
   • Convert hex to octal and binary via 4-bit binary expansion
   • Compute 9's complement as (999-864) and 10's complement as 9's complement +1
2. 7 Marks
   bRepresent the decimal number 6 in

   1. i)Excess-3 code
   2. ii)BCD code
   3. iii)Gray code
   4. iv)84-2-1 code
   5. v)2421 codes
   How to answer

   • Add 3 to decimal digit then BCD encode for Excess-3
   • Write 4-bit BCD for 6
   • Derive Gray code from binary
   • Assign weights 8-4-2--1 and 2-4-2-1 to represent 6
   • List valid code words for each code
3. 7 Marks
   aSimplify the following expression as much as possible: $F(w,x,y,z) = y'z' + w'x'z' + w'xyz' + wyz'$ and implement your result using universal gates only.
   How to answer

   • Apply Boolean algebra / K-map to simplify F(w,x,y,z)
   • Obtain minimal SOP or POS form
   • Convert simplified form to NAND-only or NOR-only form using De Morgan
   • Draw logic diagram using universal gates only
4. 7 Marks
   bExpress the following Boolean function F in a sum of min terms and a product of max terms. $F(x, y, z) = (xy + z)(y + xz)$
   How to answer

   • Expand product to canonical form using distributive law and $x+x'=1$
   • List minterms where F=1 to get sum of minterms $\Sigma m$
   • List maxterms where F=0 to get product of maxterms $\Pi M$
   • Verify complementarity of minterm and maxterm lists
5. 7 Marks
   aWhat is the role of multiplexer in the digital electronics? Explain the logic how it selects a one input among several inputs?
   How to answer

   • Define multiplexer as data selector with n select lines for 2^n inputs
   • Explain select-line decoding to enable one input to output
   • Give Boolean expression / truth table e.g. 4:1 MUX
   • Mention applications in routing, function generation
6. 7 Marks
   bWrite a short note on decoder.
   How to answer

   • Define decoder: n inputs to 2^n outputs
   • Explain enable and one-hot output operation
   • Give 2:4 or 3:8 example with truth table
   • Mention applications in memory decoding, demultiplexing
7. 7 Marks
   aDraw a full subtractor circuit using NAND gate.
   How to answer

   • State full subtractor truth table for Difference and Borrow
   • Derive Boolean expressions for D and Bout
   • Convert expressions to NAND-only form
   • Draw NAND-gate logic diagram
8. 7 Marks
   bExplain race-around condition in relation to the J-K flip-flops using timing relationships. Draw the clocked Master-Slave J-K flip-flop configuration and explain how it removes race-around condition in J-K flip-flops?
   How to answer

   • Explain J-K toggle when J=K=1 and clock width vs feedback delay causing multiple toggling
   • Show timing diagram illustrating race-around
   • Draw clocked Master-Slave J-K flip-flop configuration
   • Explain how master-slave isolation on opposite clock phases eliminates race
9. 7 Marks
   aDesign a ripple decade counter using JK flip-flop.
   How to answer

   • State decade (BCD) counting sequence 0000 to 1001
   • Use 4 JK flip-flops with ripple clocking and reset feedback on 1010
   • Draw logic diagram with NAND for reset
   • Explain working and timing
10. 7 Marks
    bDraw and explain 4-bit universal shift register.
    How to answer

    • Define universal shift register with modes hold, shift-left, shift-right, parallel load
    • Show 4-bit structure with 4x1 MUX per stage and D flip-flops
    • Explain select inputs S1 S0 operation table
    • Draw neat labelled diagram
11. 7 Marks
    aWith a neat diagram explain the operation of R-2R DAC.
    How to answer

    • Show R-2R ladder network with reference voltage and switches
    • Explain binary-weighted current division and op-amp summing
    • Derive output voltage formula $V_o = -V_{ref} \times (digital value)/2^n$
    • Draw neat labelled circuit diagram
12. 7 Marks
    bWrite a short note on PLA.
    How to answer

    • Define PLA as programmable AND-OR array
    • Explain fuse programming and product-term generation
    • Compare with PAL/PROM briefly
    • Give application example