# 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

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.