BE Computer Engineering (Pokhara University) Digital Logic (PU, ELX 110) Question Paper 2079

(a) Convert the following numbers as indicated, showing all steps: (i) $(1011.101)_2$ to its decimal and octal equivalents. (ii) $(2AF.C)_{16}$ to its binary and decimal equivalents. (6)

(b) Perform the subtraction $(110100)_2 - (10111)_2$ using the 2's complement method and verify your answer in decimal. (3)

(c) What is a weighted code? Encode the decimal number $(5290)_{10}$ in BCD (8421) and explain why the Gray code is preferred for shaft-position encoders. (3)

(a) State and prove De Morgan's theorems. Using Boolean algebra, simplify the expression $F = AB + A(B + C) + B(B + C)$ and express the result in its simplest form. (6)

(b) A logic function is given by $F(A,B,C,D) = \sum m(0,1,2,4,5,7,8,9,12,13,15)$. Use a four-variable Karnaugh map to obtain the minimal sum-of-products expression and implement it using only NAND gates. (8)

(a) Design a synchronous sequential circuit that detects the input sequence 1011 (overlapping allowed) using a Mealy model. Draw the state diagram, construct the state table, perform state assignment, and obtain the excitation equations using JK flip-flops. (10)

(b) Differentiate between a Moore machine and a Mealy machine with the help of a suitable diagram. (4)

(a) Implement the Boolean function $F(A,B,C) = \sum m(1,3,5,6)$ using an 8-to-1 multiplexer. Draw the complete connection diagram. (5)

(b) Design a 3-to-8 line decoder using logic gates and show how two such decoders can be cascaded with an enable input to build a 4-to-16 line decoder. (5)

(a) Draw the truth table of a full adder and derive the simplified expressions for the SUM and CARRY outputs. (4)

(b) Construct a 4-bit binary parallel adder using full adders and explain the limitation caused by carry-propagation delay. (4)

(a) Explain the operation of a JK flip-flop with its characteristic table and characteristic equation. What is the race-around condition and how does a master-slave configuration eliminate it? (5)

(b) Convert a D flip-flop into a T flip-flop, showing the required logic. (2)

(a) Design a MOD-6 synchronous up counter using T flip-flops and draw its timing diagram. (5)

(b) Distinguish between a synchronous counter and a ripple (asynchronous) counter. (2)

With the help of a neat logic diagram, explain the working of a 4-bit Serial-In Parallel-Out (SIPO) shift register. State two practical applications of shift registers.

(a) Express the function $F = (A + B)(A + C)$ in canonical sum-of-products (minterm) form. (3)

(b) What are universal gates? Realize the EX-OR function using only NOR gates. (3)

(a) Design a BCD-to-seven-segment decoder, listing the truth table for the segment 'a' and obtaining its simplified expression. (4)

(b) Differentiate between an encoder and a decoder. (2)

(a) Add the BCD numbers $(0101)_{BCD}$ and $(0110)_{BCD}$ and explain why a correction factor is sometimes required in BCD addition. (3)

(b) Write short notes on parity bit and its use in error detection. (2)