EXAMPLE 6.1. Encode the following binary data stream into return to zero (RZ), Non-return to zero (NRZ), AMI and Manchester codes.
Data stream: 1 1 0 0 0 0 1 0
Solution: The line coding formats for the given data stream will be as shown in figure 6.16.
diagram
FIGURE 6.16.
EXAMPLE 6.2. Draw the following data formats for the bit stream 1 1 0 0 1 1 0:
(i) Polar NRZ
(ii) Unipolar RZ
(iii) AMI
(iv) Manchester
Solution: The data formats will as shown in figure 6.17.
diagram
FIGURE 6.17 Various line codes for example 6.2.
EXAMPLE 6.3. Given that the bit sequence given below is to be transmitted
Bit sequence = 10110010
Draw the resulting waveform, if the sequence is transmitted suing:
(i) Unipolar RZ
(ii) Polar RZ
(iii) AMI
(iv) Split Phase Manchester
(v) M-ary where M = 4 (Polar quaternary)
Solution : The required waveform will be as shown in figure 6.18.
diagram
FIGURE 6.18 Waveforms for example 6.3
EXAMPLE 6.4. Which are the desirable properties of digital waveform? To transmit a bit sequence 10011011, draw the resulting waveforms using:
(i) Unipolar RZ
(ii) Unipolar NRZ
(iii) Bipolar RZ
(iv) AMI RZ
(v) Manchester.
Solution : For the properties of the line codes please study the related text.
The required waveforms have been drawn in figure 6.19.
diagram
FIGURE 6.19 Waveforms for example 6.4.
EXAMPLE 6.5. The bit sequence 1 0 1 1 1 0 1 0 1 1 is to be transmitted using following formats:
(i) Unipolar RZ and NRZ
(ii) Bipolar RZ and NRZ
(iii) Split-phase Manchester
(iv) Polar quaternary NRZ.
Solution : The required waveform will be as shown in figure 6.20.
diagram
FIGURE 6.20 Waveforms for example 6.5.
EXAMPLE 6.6. The binary data 101100110101 is transmitted over a baseband channel. Drawn the waveform for the transmitted data using following formats:
(i) Unipolar RZ
(ii) Unipolar NRZ
(iii) Bipolar RZ
(iv) Split-Phase Manchester
Compare above schemes for their BW requirements.
Solution : The required waveforms will as shown in figure 6.21.
diagram
FIGURE 6.21 Waveforms for example 6.6.
EXAMPLE 6.7. The binary data 1101010110 is transmitted over a baseband channel.
Draw the waveform for transmitted data using following format:
(i) Unipolar RZ
(ii) Polar RZ
(iii) Split Phase Manchester format
(iv) Polar quaternary NRZ signalling.
Compare above scheme for their bandwidth requirement.
Solution : The required waveform will be as shown in figure 6.22.
diagram
FIGURE 6.22 Waveforms for example 6.7.
EXAMPLE 6.8. Consider the binary sequence 0100101. Draw the waveforms for the following signalling formats:
(i) Unipolar NRZ signaling format
(ii) Bipolar RZ signaling format
(iii) AMI (alternate mark inversion) RZ signaling format.
(U.P. Tech-Semester Exa., 2002-2003)
Solution : Figure 6.23 shows all the formate.
diagram
FIGURE 6.23 Signaling formats for example 6.8.
EXAMPLE 6.8. Discuss the advantages and disadvantages of the three signaling formats illustrated in figure 6.50 of example 6.24.
Solution: The unipolar NRZ signalling format, although conceptually simple, has certain disadvantages. There are no pulse transitions for long sequences of 0 s or 1 s, which are necessary if one wishes to extract timing or synchronizing information, and there is no way to detect when and if an error has occurred from the received pulse sequence.
The bipolar RZ signalling format guarantees the availability of timing information, but there is no error detection capability.
The AMI RZ signalling format has an error detection property, if two sequential pulses (ignoring intervening 0 s) are detected with the same polarity, it is evident, it is evident that an error has occurred. However, to guarantee the availability of timing information, it is necessary to restrict the allowable number of consecutive 0 s.
EXAMPLE 6.10. Consider a binary sequence with a long sequence of 1 s followed by a single 0 and then a long sequence of 1 s. Draw the waveforms for this sequence, using the following signaling formats:
(i) Unipolar NRZ signaling
(ii) Bipolar NRZ signaling
(iii) AMI RZ signaling
(iv) Split-Phase (Manchester) signaling
Solution: Figure 6.24 shows all the required formats.
DIAGRAM
FIGURE 6.24.