PYQs Based test 20: Digital Electronics

A Boolean function F(A,B,C,D) = π(1, 5,12,15) is to be implemented using an 8×1 multiplexer (A is MSB). The inputs ABC are connected to the select inputs S₂S₁S₀ of the multiplexer respectively.



Which one of the following options gives the correct inputs to pins 0, 1, 2, 3, 4, 5, 6, 7 in order?

For the synchronous sequential circuit shown below, the output Z is zero for the initial conditions $Q_A{Q}_B{Q}_C=Q_A^{\prime }{Q}_B^{\prime }{Q}_C^{\prime }=100$.



The minimum number of clock cycles after which the output Z would again become zero is _______.

Digital input signals A, B, C with A as the MSB and C as the LSB are used to realize the Boolean function F = m₀ + m₂ + m₃ + m₅ + m₇, where mᵢ denotes the i${}^{th}$ minterm. In addition, F has a don’t care for m₁. The simplified expression for F is given by:

f(A,B,C,D) = Π M (0,1,3,4,5,7,9,11,12,13,14,15) is a max-term representation of a Boolean function f(A,B,C,D) where A is the MSB and D is the LSB. The equivalent minimized representation of this function is

Which of the following logic circuits is a realization of the function F whose Karnaugh map is shown in the figure.