GATE EC 2015 Question Paper (31-Jan-2015) (Shift 2)

A function of Boolean variables $\mathrm{x},\mathrm{y}\mathrm{and}\mathrm{z}$ is expressed in terms of the min-term as $\mathrm{F}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\mathrm{\Sigma }\left(1,2,5,6,7\right)$. Which one of the product of sums given below is equal to F(x,y,z)

The figure shows a binary counter with synchronous clear input with the decoding logic shown, the counter works as a

A 1 to 8 demultiplexer with data input Dᵢₙ, address inputs S₀, S₁, and S₂, (with S₀ as the LSB) and Y̅₀ to Y̅ ₇ as the eight de-multiplexed output, is to be designed using two 2 to 4 decoders (with enable input E and address input A₀ and A₁) as shown in the figure. Dᵢₙ, S₀, S₁, and S₂ are to be connected to P, Q, R, and S but not necessarily in this order. The respective input connections to P, Q, R, and S terminals should be

The diode in the circuit given below has V${}_{ON}$ = 0.7V but is ideal otherwise. The current (in mA) in the 4k Ω resistor is __________.

Assuming that the Op-Amp in the circuit shown below is ideal, the output voltage V₀ (in volts) is ___________________