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# GATE EC 2022: Digital Circuits Quiz 4

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Question 1

A digital system is required to amplify a binary-encoded audio signal. The user should be able to control the gain of the amplifier from a minimum to a maximum in 100 increments. The minimum number of bits required to encode, in straight binary is

Question 2

Consider the multiplexer based logic circuit shown in the figure. Which one of the following Boolean functions is realized by the circuit?

Question 3

A 4-bit shift register circuit configured for right-shift operation,  , is shown. If the present state of the shift register is ABCD = 1101, the number of clock cycles required to reach the state ABCD = 1111 is _________. Question 4

For the circuit shown in the figure, the delays of NOR gates, multiplexers and inverters are 2 ns, 1.5 ns and 1 ns, respectively. If all the inputs P, Q, R, S and T are applied at the same time instant, the maximum propagation delay (in ns) of the circuit is_______. Question 5

If X and Y are inputs and the Difference (D = X – Y) and the Borrow (B) are the outputs, which one of the following diagrams implements a half-subtractor?

Question 6

Figure I shows a 4-bits ripple carry adder realized using full adders and Figure II shows the circuit of a full-adder (FA). The propagation delay of the XOR, AND and OR gates in Figure II are 20 ns, 15 ns and 10 ns respectively. Assume all the inputs to the 4-bit adder are initially reset to 0.  At t=0, the inputs to the 4-bit adder are changed to  And The output of the ripple carry adder will be stable at t (in ns) = _______
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