GATE EC 2018 Question Paper (10-Feb-2018) (Shift 1)

Consider a binary channel code in which each code word has a fixed length of 5 bits. The Hamming distance between any pair of distinct code words in this code is at least 2. The maximum number of code words such a code can contain is ________.

A binary source generates symbols 𝑋 ∈ {−1, 1} which are transmitted over a noisy channel. The probability of transmitting 𝑋 = 1 is 0.5. Input to the threshold detector is 𝑅 = 𝑋 + 𝑁. The probability density function *f${}_N$ *(𝑛) of the noise 𝑁 is shown below:



If the detection threshold is zero, then the probability of error (correct to two decimal places) is ________.

A p-n step junction diode with a contact potential of 0.65 V has a depletion width of 1 μm at equilibrium. The forward voltage (in volts, correct to two decimal places) at which this width reduces to 0.6 μm is ________.

A traffic signal cycles from GREEN to YELLOW, YELLOW to RED and RED to GREEN. In each cycle, GREEN is turned on for 70 seconds, YELLOW is turned on for 5 seconds and the RED is turned on for 75 seconds. This traffic light has to be implemented using a finite state machine (FSM). The only input to this FSM is a clock of 5 second period. The minimum number of flip-flops required to implement this FSM is ________ .

There are two photolithography systems: one with the light source of wavelength λ₁ = 156 nm (system 1) and another with the light source of wavelength λ₂ = 325 nm (System 2). Both photolithography systems are otherwise identical. If the minimum feature sizes that can be realized using System1 and System2 are L${}_{min1}$ and L${}_{min2}$ respectively, the ratio L${}_{min1}$ /L${}_{min2}$ (correct to two decimal places) is________.