GATE EC 2021 Question Paper (07-Feb-2021) (Shift 2)

The propagation delays of the XOR gate, AND gate, and multiplexer (MUX) in the circuit shown in the figure are 4 ns, 2 ns, and 1 ns, respectively.



If all the inputs P, Q, R, S, and T are applied simultaneously and held constant the maximum propagation delay of the circuit is

The content of the registers are R₁ = 25H, R₂ = 30H and R₃ = 40H. The following machine instructions are executed.

PUSH{R1}

PUSH{R2}

PUSH{R3}

POP{R₁}

POP{R2}

POP{R3}

After execution, the content of registers R1, R2, R3 are

The electrical system shown in the figure converts input source current iₛ(t) to output voltage v₀(t).



Current i${}_L$ (t) in the inductor and voltage v${}_c$ (t) acros the capacitor are taken as the state variables, both assumed to be initially equal to zero, i.e., i${}_L$ (0) = 0 and v${}_c$ (0) = 0. Then system is

A digital transmission system uses a (7, 4) systematic linear Hamming code for transmitting data over a noisy channel. If three of the message-codeword pairs in this code (mᵢ ; cᵢ), where cᵢ is the codeword corresponding to the i${}^{th}$ message mᵢ, are known to be (1 1 0 0 ; 0 1 0 1 1 0 0), (1 1 1 0 ; 0 0 1 1 1 1 0) and (0 1 1 0 ; 1 0 0 0 1 1 0), then which of the following is a valid codeword in this code?

The impedance matching network shown in the figure is to match a lossless line having characteristic impedance Z₀ = 50 Ω with a load impedance Z${}_L$. A quarter-wave line having a characteristic impedance Z₁ = 75 Ω is connected to Z${}_L$. Two stubs having characteristic impedance of 75 Ω each are connected to this quarter-wave line. One is a short-circuited (S.C.) stub of length 0.25 λ connected across PQ and the other one is an open-circuited (O.C.) stub of length 0.5 λ connected across RS.



The impedance matching is achieved when the real part of Z${}_L$ is