Digital Communications Quiz with solutions



  1. The band width  needed to transmit Television video plus audio signals of bandwidth 4.2 MHz using Binary PCM  quantization level of 512 is (  c     )         a. 2 MHz            b. 25.6MHz                        c.37.8MHz                    d.75.6MHz
  2. A signal m(t)has a bandwidth of 1.0 KHz and exhibits a maximum rate of change of 2.0 volts/sec. The signal is sampled at a sampling frequency of 20 KHz and quantized using delta modulator. The minimum step size to avoid slope overload is (  b    )                                                                                                                      a. 1.0mV        b. 0.1mV                c.10.0mV                      d.0.01mV
  3. For a 10 bit PCM system, the signal to Quantization noise ratio is 62 dB. If the number of bits are increased by 2, then the signal to Quantization noise ratio will be (  c      )                                                                                                                    a. Increased by 6 dB                                   b.  Decrease by 6 dB                                       c. Increased by 12 dB                                  d. Decrease by 12 dB
  4. Write the condition to eliminate slope overload error in a Delta modulation system—————————
  5. Write the condition to eliminate slope overload error in a Delta modulation system if the input is a single-tone signal—————————
  6. For which value of A , A-law has linear transfer characteristics——————–.
  7. For which value of µ , µ-law has linear transfer characteristics——————–.
  8. In a PCM system if the step size is 5V , then the Quantization noise in dB is   (  d    )                                                                                                                                             a. -5 dB.          b. -3.18dB       c. -10dB                      d. 3.18dB.
  9. Draw the characteristics of Mid-rise and Mid-tread type Quantizers ————–
  10. The maximum slope of the signal ———————-
  11. The sampling rate of the signal ————————–
  12. The step size in a 8- bit pcm system if the input signal to PCM is oscillating between [+4V,-4V] is—————————–



  1. Entropy is a measure of ——————————– 3M.  
  2. The capacity of a band – limited AWGN channel in terms of kbps if the average received signal power to noise power spectral density is 1000 and the bandwidth is approximately infinite is (  a    )   [Hint: Shannon’s bound Cinfinity =  S/No]                                                                                                                        a.  1.44        b. 1.08                                c. 0.72                           d. 0.36
  3. If Y= g(X) where g denotes a deterministic function, then the conditional entropy H(Y/X) is (  b ) 3M.                                                                                                           a. ≠ 1         b.  = 0                           c. = 1                           d. ≠ 0
  4. A Source generates three symbols with probability of 0.25, 0.25, and 0.50 at a rate of 3000 symbols per second. Assuming the symbols are generated independently from the source, the most efficient source encoder would have average bit rate of ( b ) 4M.                                                                                             a. 6000 bits/sec                                                         b. 4500 bits/sec                                 c. 3000 bits/sec                                                         d. 1500 bit/sec.
  5. A source generates four equi-probable symbols. If the source coding is adopted, the average length of the code for 100% efficiency is ( c )                       a. 6 bits / symbol                                                          b.   3 bits / symbol                           c.  2 bits / symbol                                                        d.  4 bits / symbol
  6. Draw the channel diagram of Binary Erasure channel and write its channel matrix ………………………..
  7. For a Binary Symmetric Channel the entropies of X & Y are if the conditional probability p=0.5, where X & Y are input & output random variables of BSC  (   d     )3M                                                                                                                          a. 1,0           b. 0,0               c. 0,1                           d. 1,1
  8. Match the following   (  d    )                                                                                                       a. Lossless channel                                           1.  only one non-zero element in each row                                                                                                                                        b. Deterministic channel                                2. Only one non-zero element in each row and each column.                                                                                                   c. Noiseless channel                                           3. Only one Non-zero element in each column.                                                                                                                                d. for a noiseless channel                                  4. H(Y/X)=0 and H(X/Y)= 0. a. none of these                                                  b.   b-3,c-4,a-1,d-2                                    c. c-4,d-3,a-1,b-2                                             d.  b-1,c-2,a-3,d-4.
  9. Given a Binary Symmetric Channel, the expression for Entropy is (pis conditional probability of error   ——————- 3M.  

Digital Communications Unit-3 Quiz with Solutions



  1. The number of Parity check bits in an (n, k) Linear Block codes are (    b      )      a.n                b. (n-k)                       c.  (n+k)                       d. k
  2. The Hamming Weight of the following code words 10011101 & 00111100 is      (   c   ) 2M.                                                                                                                                       a. None of these      b. 4, 5              c.5, 4                           d.3,4
  3. A cyclic code can be generated using———————— and A block can be generated using——————-.(   c   )                                  a.Generator matrix & Generator polynomial.                                                          b.Generator matrix & Generator matrix.                                                            c.Generator polynomial & Generator matrix.                                                            d.None of the above.
  4. The rate of a Block code is the ratio of(    c     )                                                                a.Message length to Block length.                 b.Block length to message length.  c.Message weight to Block length.                 d.None of the mentioned.
  5. The syndrome in LBC is calculated using , where Y represents received code word   (     a       ) 2M                                                                                                                      a. S= Y HT          b. S = YH                    c. S= YT H                  d. S= YT HT
  6.  A non-Zero value of Syndrome in a Block code represents ( b    ) 2M.                  a.No error during transmission.     b.An error occurred during transmission.   c.Both a and  b                                         d.None of the above.
  7. The transmitted code word(X) in an LBC can be obtained from received code word( Y) by using the equation (  a   ), where E represents error vector.              a. X= E + Y           b.  X = X.Y                  c. X= E.Y                    d. X= X/Y
  8. The parity check matrix of a (6,3) block code if Generator matrix is G  3M.             ——————-.
  9. In the above question find the Code words corresponding to message vectors [110] and [111]——————-. Ans: [110110], [111000].
  10. For the Q.8. Find the syndrome value when the received code word is 001111—-4MAns: syndrome value [0 0 1]
  11. For a (7,4) cyclic code , the generator polynomial is given as find the codeword  for the data 1100       Non systematic codeword is—————- .Ans:  1011100              Systematic codeword is——————–.Ans: 1011100.



    1. The modulation technique that provides minimum probability of error is (  b   ). a. ASK                  b. PSK                   c. DPSK                        d.FSK
    2. At a given probability of error, binary coherent FSK is inferior to binary coherent PSK by (  c  )                                                                                                         a. 6 dB                b. 2 dB           c.  3 dB           d.  0 dB             e. None of these.
    3. If Eb, the energy per bit of a binary digital signal, is 10-5watt-sec and the one-sided power spectral density of the white noise, No= 10-6 W/Hz, then the output SNR of the matched filter is  (   d    )                                               a. 26 dB         b.  20 dB          c. 10 dB          d. 13 dB          e. None of these
    4. In which system, bit stream is portioned into even and odd stream (   c   )  a. BPSK                  b.  MSK            c. QPSK                     d.  FSK
    5. Optimum filter can be called as———when the input noise is white noise (  a   ) 2M.                                                                                                                        a. Matched filter   b.  High pass filter        c. Low pass filter      d. None of these
    6. The probability of error of ASK is ————————————.
    7. The probability of error of FSK is ————————————.
    8. Write the expression for QPSK modulation —————————————-2M.
    9. Draw the block diagram of DPSK system————————————.
    10. A pulse g(t) = A cos(πt/2T) for 0 ≤ t ≤ T is transmitted over an AWGN channel with two sided noise power spectral density No/2 Watts/Hz. The impulse response of the matched filter is (  a     )                                                           a. A sin (πt/2T)                                                            b.   A rec (πt/2T)                           c. A rec (π(T-t)/2T)                                                    d. A sin (π(T-t)/2T)           
    11. If the probability of error function of a modulation scheme is Pe = (½) erfc(x) thenthe same Pe interms of Q-function is ( b   )                                             a. Q ( 31/2 * x)                    b. Q (21/2 * x)                c. Q(x)             d. none of these.



Author: Lakshmi Prasanna Ponnala

Completed M.Tech in Digital Electronics and Communication Systems.

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