# RTU Previous Exam Papers BE CS 3rd Semester

# Digital Electronics Feb-2011

1. a) Convert the decimal number 250.5 to base 3, base 4 and base 7.

b) Find the 10’s complement of (935)_{ir}

c) Find the equivalent Gray Code for (478)_{10}.

d) Obtain the weighted binary code for base -10 digits using weights of5421

e) Find the complement of the following Boolean functions by finding dual of them:

i) F {A,B,C) = (A + B’ + C){A + B’){B + C)(A + B + C) .

ii) F(w, x, y, z) = y’z + wxy’ + wxz’ + w’x’z .

**OR**

a) Represent the decimal number 2047 as

i) Radix – 2 number

ii) BCD code

in) 8, 4, -2, -1 code

iv) Excess -3 code

b) Represent (-17)_{]0} in

i) S/gnMagnitude form

ii) Vs complement representation

c) Find the radix V for the following equations to be valid:

**OR**

a) The following boolean expression F – Z(w’ + y) is a simplified version of the expression F = (w’ + y)(x’ + zXw’ + z) Find the don’t care conditions, if any.

b) Simplify the following boolean function, using the don’t care conditions d, with K-map and realize the simplified expression with NOR gates only.(8)

F = A’B’D’ + A’CD + A’BC d = A’BC’D+ACD+AB’D’

c) Express the function

F = A+~BC

i) in canonical SOP form

ii) in canonical POS form.

**Unit-IV**

4. a) Design a 4-bit parallel ADDER/SUBTRACTOR circuit with ADD/SUB control line.

b) Design and implement a Full-Subtractor circuit using 3-to-8 decoder and external gates.

c) Design and implement a combinational circuit for addition of two one-digit BCD numbers.

**OR**

a) Implement the following function using a multiplexer having two select lines A and B. F(A, B, C,D) = X _{m}(l, 3, 5, 6, 9,11,13, 15).

b) Construct a 5×32 decoder with four 3×8 decoders and a 2×4 decoder.

c) For three – inputs, prove that Exclusive – OR function and Equivalence function, both are same.

**Unit-V**

5. a) Design a Synchronous counter using D-flip flops for the following binary sequence :0, 1,3, 7, 6, 4 and repeat.

b) Design a 4 – bit, Mode – controlled Bidirectional shift register using SR flip flops and explain its working in both directions.

**OR**

a) Design an asynchronous Decade Counter. Explain the steps of designing and draw its state diagram also.

b) Reduce the state – table given below and draw the state – diagram for reduced table.