Switching Circuits and Logic Design: Week 6: Assignment 6:

1. For a 6-variable binary decision diagram, the maximum number of non-terminal nodes can be  ……………

Ans: 63

2. For an n-variable binary decision diagram, the maximum number of terminal nodes can be:
 a. n
 b. 2n
 c. 2^n
 d. None of these

Ans: c

3. Which of the following is true for a ROBDD?
 a. The number of nodes can vary widely depending upon the ordering of the variables.
 b. The representation is unique for a given variable ordering.
 c. It is very useful to determine whether two functions are equivalent.
 d. All of these.

Ans: d

4. Which of the following statements are true?
 a. A non-terminal node of the BDD can be implemented using an EXOR gate.
 b. A non-terminal node of the BDD can be implemented using a 2-to-1 multiplexer.
 c. From the BDD representation of the function, we can directly generate a MUX realization.
 d. None of these.

Ans:b,c

5. Which of the following is a correct Shannon decomposition of the function F(A,B,C) = A’.B + B.C’ + A.B’.C ?
 a. F = B’.(A’.0 + 0.C’ + A.1.C) + B.(A’.1 + 1.C’ + A.0.C)
 b. F = B’.(A’.1 + 1.C’ + A.0.C) + B.(A’.0 + 0.C’ + A.1.C)
 c. F = B’.(A’.B + B.C’) + B.(B.C’ + A.B.C)
 d. None of these

Ans: a

6. Which of the following identities are wrong?
a. (x⊕y)⊕z=x⊕(y⊕z)
b. (x+y)⊕z=x⊕(y+z)
c.  x ⊕ y = y + x if x.y = 0
d. None of these

Ans: b

7. What will be the Reed-Muller form for the function f(A,B,C) = ∑ (0, 3, 5, 6)?
a. 1⊕AB⊕BC⊕CA
b. 1⊕A⊕B⊕C
c. 1⊕A⊕BC
d. None of these

Ans: b

8. Which of the following expansions are correct?
  a. f(x1, x2....,xn) = x2fx2=1⊕x2'fx2=0
  b. f(x1, x2....,xn) = fx1=0⊕x1(fx1=0⊕fx1=1)
  c. f(x1, x2....,xn) = xn'(fxn=0⊕fxn=1)⊕fxn=0
  d. All of these.

Ans: d

9. What will be the possible threshold (T) and weights(w1 & w2) for realizing 2-input NAND function
 a. T=2, w1 =1, w2=-1
 b. T=-1, w1=-0.7, w2=-0.7
 c. T=0, w1=-0.5, w2=-0.5
 d. None of these

Ans: b

10. Which of the following is true for a threshold gate?
 a. Different functions can be realized just by changing the weights and threshold values.
 b. A threshold gate can realize any Boolean function.
 c. The weights must be positive valued.
 d. None of these.

Ans: a