The propagation delay of the $2 \times 1$ MUX shown in the circuit is 10 ns. Consider the propagation delay of the inverter as 0 ns. 
If S is set to 1 then the output Y is ____________.
To determine the behavior of the output \( Y \) when the select line \( S \) is set to \( 1 \), we must analyze the feedback path of the circuit.
1. Circuit Logic Analysis
- The circuit uses a \( 2 \times 1 \) Multiplexer (MUX). The output equation of a \( 2 \times 1 \) MUX is: \( Y = \overline{S} \cdot I_0 + S \cdot I_1 \)
- When \( S = 1 \), the MUX selects input \( I_1 \).
- Input \( I_1 \) is connected to the output \( Y \) via an inverter (NOT gate).
- Therefore, the logical operation of the circuit becomes: $$Y_{next} = \overline{Y_{current}}$$
This configuration, where the output is fed back to the input with an odd number of inversions, forms a ring oscillator. The output will continuously toggle between '0' and '1', creating a square wave.
2. Determining the Time Period (\( T \))
The time taken for the output to complete one full cycle (going from \( 0 \rightarrow 1 \rightarrow 0 \)) is twice the total propagation delay of the feedback loop.
- Propagation delay of MUX (\( t_{MUX} \)) = \( 10 \text{ ns} \)
- Propagation delay of Inverter (\( t_{Inv} \)) = \( 0 \text{ ns} \)
- Total delay for a single transition (\( \Delta t \)) = \( t_{MUX} + t_{Inv} = 10 \text{ ns} + 0 \text{ ns} = 10 \text{ ns} \)
A full cycle consists of two transitions (low-to-high and high-to-low):
$$T = 2 \times \Delta t = 2 \times 10 \text{ ns} = 20 \text{ ns}$$
3. Calculating the Frequency (\( f \))
The frequency is the reciprocal of the time period:
$$f = \frac{1}{T}$$ $$f = \frac{1}{20 \times 10^{-9} \text{ s}}$$ $$f = \frac{10^9}{20} \text{ Hz} = 50 \times 10^6 \text{ Hz}$$ $$f = 50 \text{ MHz}$$
Final Conclusion
Since the output toggles with a calculated frequency of \( 50 \text{ MHz} \), the correct choice is:
A square wave of frequency 50 MHz
Important Questions from Multiplexer
The device which changes from serial data to parallel data is:
Consider a logic gate circuit. with 8 input lines (D 0, D 1..... D 7) and 3 output lines (A 0, A 1, A 2) specified by following operations
A 2= D 4+ D 5+ D 6+ D 7
A 1= D 2+ D 3+ D 6+ D 7
A 0= D 1+ D 3+ D 5+ D 0
Where + indicates logical OR operation. This circuit is
Which of the following statements are true?
A. Frequency division multiplexing technique can be handled by digital circuits.
B. Time division multiplexing technique can be handled by analog circuits
C. Wavelength division multiplexing technique is used with optical fiber for combining two signals.
D. Frequency division multiplexing technique can be applied when the bandwidth of a link is greater than the bandwidth of the signals to be transmitted.
Choose the correct answer from the options given below :
Consider the sentence below.
There is a country that borders both India and Pakistan.
Which of the following logical expressions express the above sentence correctly when the predicate Country(x) represents that x is a country and Borders(x, y) represents that the countries x and y share the border?
A digital computer has a common bus system for 8 registers 16 bits each. How many multiplexers are required to implement common bus? What size of multiplexers is required?
