Digital Logic (DL)

Q:   In 16-bit 2’s complement representation, the decimal number −28 is:

• A:  1111 1111 0001 1100
• B:  0000 0000 1110 0100
• C:  1111 1111 1110 0100
• D:  1000 0000 1110 0100

Q:   Which one of the following is NOT a valid identity?

• A:  (x⊕y)⊕z=x⊕(y⊕z)/li>
• B:  (x+y)⊕z=x⊕(y+z)
• C:  x⊕y=x+y,ifxy=0
• D:  x⊕y=(xy+x′y′)′

Q:   Consider Z = X – Y, where X, Y and Z are all in sign-magnitude form. X and Y are each represented in n bits. To avoid overflow, the representation of Z would require a minimum of:

• A:  n bits
• B:  n - 1 bits
• C:  n + 1 bits
• D:  n + 2 bits

Q:   Consider three 4-variable functions f1, f2, and f3, which are expressed in sum-of-minterms as f1 = ∑(0, 2, 5, 8, 14), f2 = ∑(2, 3, 6, 8, 14, 15), f3 = ∑(2, 7, 11, 14) For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as:

• A:  ∑ (7, 8, 11)
• B:  ∑(2, 7, 8, 11, 14)
• C:  ∑(2, 14)
• D:  ∑(0, 2, 3, 5, 6, 7, 8, 11, 14, 15)

Q:   What is the minimum number of 2-input NOR gates required to implement a 4-variable function expressed in sum-of-minterms form as f = Σ(0, 2, 5, 7, 8, 10, 13, 15)? Assume that all the inputs and their complements are available _______________.

Q:   Consider the sequential circuit shown in the figure, where both flip-flops used are positive edge-triggered D flip-flops.
The number of states in the state transition diagram of this circuit that have a transition back to the same state on some value of “in” is _____.

Q:   Consider the unsigned 8-bit fixed point binary number representation below,
b7 b6 b5 b4 b3 . b2 b1 b0
where the position of the binary point is between b3 and b2. Assume b7 is the most significant bit. Some of the decimal numbers listed below cannot be represented exactly in the above representation:
(i) 31.500 (ii) 0.875 (iii) 12.100 (iv) 3.001
Which one of the following statements is true?

• A:  None of (i), (ii), (iii), (iv) can be exactly represented
• B:  Only (ii) cannot be exactly represented
• C:  Only (iii) and (iv) cannot be exactly represented
• D:  Only (i) and (ii) cannot be exactly represented

Q:   Consider the minterm list form of a Boolean function F given below.
F(P,Q,R,S)=∑m(0,2,5,7,9,11)+d(3,8,10,12,14)
Here, m denotes a minterm and d denotes a don’t care term. The number of essential prime implicants of the function F is ______.

Q:   The representation of the value of a 16-bit unsigned integer X in hexadecimal number system is BCA9. The representation of the value of X in octal number system is

• A:  571244
• B:  736251
• C:  571247
• D:  136251

Q:   Given the following binary number in 32-bit (single precision) IEEE-754 format:
00111110011011010000000000000000
The decimal value closest to this floating-point number is

• A:  1.45×10
• B:  1.45×10^-1
• C:  2.27×10^-1
• D:  2.27×10