Paper 11

Core XI: Digital Systems

Old CBCS Core X
(IC’s and scales of Integration, Digital Circuits and their realization, Boolean Algebra, Truth tables, Equivalent Circuits, Theory and application of CRO, Data processing circuits, Arithmetic Circuits, different types of Timers: IC 555, knowledge of computer organization, Shift registers and counters.)

Syllabus

Unit 1
  • Integrated Circuits (Qualitative treatment only): Active and Passive Components, Discrete components, Wafer Chip, Advantages and Drawbacks of ICs, Scale of Integration: SSI, MSI, LSI and VLSI (basic idea and definitions only), Classification of ICs, Examples of Linear and Digital ICs.
  • Digital Circuits: Difference between Analog and Digital Circuits, Binary Numbers, Decimal to Binary and Binary to Decimal Conversation, BCD, Octal and Hexadecimal numbers, AND, OR and NOT Gates (realization using Diodes and Transistor), NAND and NOR Gates as Universal Gates, XOR and XNOR Gates and application as Parity Checkers.
Unit II

Boolean algebra: De Morgan’s Theorems: Boolean Laws, Simplification of Logic Circuit using Boolean Algebra, Fundamental Products, Idea of Minterms and Maxterms, Conversion of truth table into Karnaugh Map and SOP and POS simplification. Universal logic implementation (NAND & NOR).

Unit III
  • Data Processing Circuits: Basic Idea of Multiplexers, De-multiplexers, Decoders, Encoders.
  • Arithmetic Circuits: Binary Addition. Binary Subtraction using 2s complement. Half and Full Adders. Half and Full Subtractors, 4 bit binary Adder/Subtractor.
  • Timers: IC 555: block diagram and application is Astable multivibrator and Monostable multivibrator.
Unit IV
  • Introduction to Computer Organization: Input/output Devices, Data storage (idea of RAM and ROM), Computer memory, Memory organization and addressing, Memory Interfacing, Memory Map.
  • Shift registers: Serial-in-serial-out, Serial-in-Parallel-out, Parallel-in-Serial- out and Parallel-in- Parallel-out. Shift Registers (only up to 4 bits)
  • Counters (4 bits): Ring Counter, Asynchronous counters, Decade Counter. Synchronous Counter.
Text Books
  • Digital Circuits and Logic design: Samuel C. Lee (Printice Hall)
  • Digital Principles and Applications - A. P. Malvino, D. P. Leach and Saha (Tata Mc Graw)
Reference Books:
  • The Art of Electronics by Paul Horowitz and Wilfield Hill, Cambridge University
  • Electronics by Allan R. Hambley, Prentice Hall 3. Principles of Electronics V. K. Mehta and Rohit Mehta (S. Chand Publishing)
  • Digital Logic and Computer design M. Morris Mano (Pearson)
  • Concepts of Electronics D. C. Tayal (Himalaya Publishing house)
  • Digital System and Application, Gupta Kumar, Pragati Prakashan

Questions

2025 | +3-IV-S-CBCS(MS)-Sc(H)-Core-X-Phy-R&B | Full Mark 60

PART-I | Answer all the questions | 1x8
  • The binary equivalent of decimal number 9 is _____.
  • The boolean expression $Y=A \oplus B$ represent _____ gate.
  • ______ memory is non volatile and written only once.
  • The 2's complement of binary number 1011 is _____.
  • The speed of 48 x ROM is _____ kbps.
  • The deflection sensitivity of CRO is directly proportional to the length of deflecting plates. (True/False/Uncertain)
  • A wafer is a thin slice of a good conducting material. (True/False/Uncertain)
  • How many output lines are there in a full adder ?
PART-II | Answer any eight within two to three sentences | 1.5 ×8
  • Convert $(48)_8$ into decimal number system.
  • Evaluate $A( \overline{A}+B)$ using truth table.
  • Design the circuit to obtain AND gate from NOR gate.
  • Define minterm and write an example.
  • What is synchronous counter ?
  • Whatis demultiplexer?
  • What is Hard disk ?
  • Distinguish between active and passive circuit components.
  • Write notes on semiconductor memory cell.
  • Write three applications of CRO.
PART-III | Answer any eight of the following in maximum 75 words. | 2× 8
  • Subtract $(1101)_2$ from $(1010)_2$ by 2's complement method.
  • Convert 324.135 to hexadecimal number.
  • Using Logic circuit discuss about 4-to-1 multiplexer.
  • What is necessity of time base voltage in CRO ?
  • Solve using k-map $$Y = A\overline{BC}+ \overline{AB}C+AB\overline{C}+\overline{A}BC$$
  • Write a note on RAM.
  • State and prove Demorgan's theorem.
  • Compare between Analog and digital circuits.
  • Find the decimal equivalent of minterm $\overline{A}B\overline{C}$.
  • Explain half subtractor circuit by using truth table.
PART-IV | Answer within 500 words each. | 6×4

  1. Discuss about the fabrication of diodes, Transistors, Resistors and capacitors on monolithics ICs.

    OR

    Using DTL circuit describe the function of NOR gate and NAND gate.

  2. Explain the K-Map method for simplification of boolean expressions having four variables.

    OR

    Discuss the construction of cathode ray tube. Obtain its deflection sensitivity.

  3. Describe half adder and full adder with their ligic symbol, circuit and truth table.

    OR

    With logic circuit discuss the function of IC 555 Timer and how it is used as Astable multivibrator.

  4. What is shift register ? Notes on the operation of SISO and SIPO shift registers.

    OR

    What is a Counter ? Explain the operation of decade counter.nd prove Ehrentest's Theorem.
    and SIPO shift registers.

    OR

    What is a Counter ? Explain the operation of decade counter.nd prove Ehrentest's Theorem.

    OR

    Define expectation value of a dynamical variable. Give expression for expectation value of position and momentum.

6) Derive an expression for Boundary conditions using Schrodinger's quation to one dimensional square well potential.

OR

Derive an expression for quantum mechanical tunneling across a rectangular potential barrier.

7) Explain Normal Zeeman effect using classical theory and also obtain an expression for Zeeman shift.

OR

State and explain Larmour's Theorem. Then derive an expression for Larmor's frequency.

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