Question:medium
A source transmits symbols from an alphabet of size 16. The value of maximum achievable entropy (in bits) is____.
A source transmits symbols from an alphabet of size 16. The value of maximum achievable entropy (in bits) is____.
Show Hint
Maximum entropy occurs when all symbols in the alphabet are equally likely. Use \(\log_2 N\) to calculate maximum entropy for a source with \(N\) symbols.
Updated On: Feb 12, 2026
Show Solution
Correct Answer: 4
Solution and Explanation
The entropy of a source is a measure of the uncertainty or information content associated with a random variable. For a source transmitting symbols from an alphabet of size \( n \), the maximum entropy \( H_{\text{max}} \) can be calculated using the formula:
\( H_{\text{max}} = \log_2 n \)
In this problem, the alphabet size is 16. Substituting this value into the formula:
\( H_{\text{max}} = \log_2 16 \)
Knowing that \( 16 = 2^4 \), we can simplify the expression:
\( H_{\text{max}} = 4 \)
The computed maximum entropy is 4 bits. Checking the provided range (4,4), we confirm that the calculated value lies within the expected range.
Was this answer helpful?
0
Top Questions on Impedance transformation
- A digital communication system transmits through a noiseless bandlimited channel \([-W, W]\). The received signal \(z(t)\) at the output of the receiving filter is given by: \[ z(t) = \sum_n b[n] x(t - nT), \] where \(b[n]\) are the symbols and \(x(t)\) is the overall system response to a single symbol. The received signal is sampled at \(t = mT\). The Fourier transform of \(x(t)\) is \(X(f)\). The Nyquist condition that \(X(f)\) must satisfy for zero intersymbol interference at the receiver is:
- GATE EC - 2024
- Electromagnetics
- Impedance transformation
- Consider the Earth to be a perfect sphere of radius \(R\). Then the surface area of the region, enclosed by the \(60^\circ N\) latitude circle, that contains the north pole in its interior is \(\_\_\_\_\).
- GATE EC - 2024
- Electromagnetics
- Impedance transformation
- A uniform plane wave with electric field: \[ \vec{E}(x) = A_y \hat{a}_y e^{-\frac{j2\pi x}{3}} \, {V/m}, \] is traveling in the air (relative permittivity, \(\epsilon_r = 1\), and relative permeability, \(\mu_r = 1\)) in the \(+x\) direction. It is incident normally on an ideal electric conductor (conductivity, \(\sigma = \infty\)) at \(x = 0\). The position of the first null of the total magnetic field in the air (measured from \(x = 0\), in meters) is \(\_\_\_\_\).
- GATE EC - 2024
- Electromagnetics
- Impedance transformation
- Let \(z\) be a complex variable. If \(f(z) = \frac{\sin(\pi z)}{z^2 (z - 2)}\) and \(C\) is the circle in the complex plane with \(|z| = 3\), then: \[ \oint_C f(z) \, dz \] is \(\_\_\_\_\).
- GATE EC - 2024
- Electromagnetics
- Impedance transformation
- Want to practice more? Try solving extra ecology questions todayView All Questions
