Digital Systems (CS-304) - Important Questions

What are logic gates? Describe the different types of logic gates.

Convert given numbers between various bases and codes (binary, octal, decimal, hexadecimal, Gray, BCD, Excess-3).

Convert base-7 to decimal/hexadecimal, decimal to octal/base-4, hexadecimal to octal/binary, and find 9's and 10's complement.

Represent the decimal number 6 in Excess-3, BCD, Gray, 84-2-1 and 2421 codes.

Simplify $F(w,x,y,z) = y'z' + w'x'z' + w'xyz' + wyz'$ and implement the simplified result using universal gates only

Simplify a given SOP Boolean function using K-map.

Implement a given Boolean function using only NAND gates

Simplify the Boolean function $F(W,X,Y,Z) = WX'(Y' + Z') + X'Z'(W' \odot Y)$ to minimal SOP using Boolean algebra and implement it using NOR-NOR logic.

Find prime implicants, essential prime implicants and minimal SOP for given 4-variable function with don't cares and check uniqueness.

Given $f_1$ and $f_2$ with don't-care terms, find $f_3 = f_1 \cdot f_2$ and $f_4 = f_1 + f_2$ and determine how many functions each represents

Given network with $f_1 = xz + x'z'$ and overall transmission $f(w,x,y,z)$, determine functions $f_2$ and $f_3$

Design a combinational logic circuit to convert BCD to Excess-3 code.

Implement a given Boolean function using a multiplexer such as $4{:}1$, $8{:}1$ or $16{:}1$ MUX.

What is a multiplexer, its role, and how it selects one input among several inputs, including $8{:}1$ multiplexer with truth table and expression.

Write a short note on decoder.

Draw a full subtractor circuit using NAND gates.

What is an encoder? Design and explain a decimal-to-BCD encoder.

Explain the working of a full adder with truth table and logic diagram and its need in arithmetic circuits.

Design an $8 \times 1$ multiplexer using smaller multiplexers.

Design a $3 \times 8$ decoder using one $1 \times 2$ decoder and two $2 \times 4$ decoders with Enable input.

Draw a schematic for a minimal circuit that uses only NOR gates that performs the two's complement operation on a four bit input value. Let the input be $A_{3:0}$ and the output be $B_{3:0}$.

Design and implement a full adder circuit, including design steps and implementation using two half adders and an OR gate.

Design a Half adder circuit with truth table and logic diagram.

Implement given Boolean functions $F_1, F_2$ using a decoder and external gates.

Describe the 4-bit universal shift register with a neat diagram.

Explain the working of the master-slave J-K flip-flop.

Explain race-around condition in J-K flip-flop and how master-slave configuration removes it.

Design a ripple decade counter using JK flip-flops.

Write a short note on PLA.

Design a 3-bit/4-bit binary UP/DOWN counter with direction control using T flip-flops, with timing diagram.

Explain asynchronous (ripple) counters and synchronous counters and compare them with respect to speed and hardware complexity.

Implement the given Boolean functions using PLA and draw the PLA programming table.

Draw the state diagram for the given Even/Odd sequential system specification with inputs $x(t), y(t)$, output $z(t)$, and transition/output functions.

Design a synchronous counter to count in the random sequence $0, 2, 4, 5, 7, 0, \dots$ using D flip-flops.

Design a sequential circuit using T flip-flop for the given state table.

Explain edge triggering and differentiate SR flip-flop and JK flip-flop with functional operation and excitation tables.

Explain the need for interfacing between TTL and MOS logic and how TTL-to-MOS/CMOS interfacing is achieved.

Explain the principle and working of a sample and hold circuit with diagram and its need in ADC systems.

Explain the operation of R-2R ladder DAC with neat diagram.

Draw the circuit diagram of a Schmitt trigger and explain its working.

Explain the internal block diagram and working of the IC 555 timer and discuss two applications.

Write short notes on A/D and D/A converters, CMOS logic, Shannon channel capacity theorem, and Nyquist sampling theorem.

Describe the circuit, performance and characteristics of a CMOS inverter.

Draw and explain PMOS, NMOS and CMOS logic families.

Explain the working of a Schmitt trigger with a neat diagram and design it for given upper and lower threshold voltages and saturation voltages.

Determine the number of bits $n$ required for an ADC with given voltage range and accuracy/resolution.

With the help of circuit diagram explain the working of V-F converters.

Derive the frequency of oscillation of an astable multivibrator using the IC 555 timer.

Explain the concept and working principle of Time Division Multiplexing (TDM) with block diagram, including multiplexing basics and synchronous vs asynchronous TDM.

Explain the quantization process and quantization error/noise in PCM and how quantization noise can be reduced.

Explain the Pulse Code Modulation (PCM) system with a neat block diagram.

Explain the geometrical / signal-space representation of non-orthogonal BFSK.

Define mutual information, relate it to channel capacity, and compute the Shannon limit for a voice-band channel with given SNR and bandwidth.

Explain the BFSK modulation scheme and its working.

Explain the working of the BPSK modulation scheme with the help of a block diagram.