Question

We need to use synchronous tdm and combine 20 digital sources, each of 100 kbps. each output slot carries 2 bit from each digital source, but one extra bit is added to each frame for synchronization. answer the following questions:

a. what is the size of an output frame in bits?
b. what is the output frame rate?
c. what is the duration of an output frame?
d. what is the output data rate?
e. what is the efficiency of the system (ratio of useful bits to the total bits).

Answer 1

The size of an output frame is 41 bits, the output frame rate is 50,000 frames per second, the duration of an output frame is 20 microseconds, the output data rate is 2.05 Mbps, and the efficiency of the system is approximately 97.56%.

Step-by-step explanation:

To answer these questions, we need to consider the principles of Time Division Multiplexing (TDM).

1. Size of an output frame: Each digital source contributes 2 bits per output slot, and there are 20 sources, so that's 40 bits. Plus, there is an additional synchronization bit added to each frame, making the total number of bits 41 per frame.
2. Output frame rate: Each source is 100 kbps, so 100,000 bits are transmitted every second per source. Since there are 2 bits per source per frame, it takes 1/50,000 of a second to transmit one frame per source. The output frame rate is therefore 50,000 frames per second because each frame must represent all 20 sources.
3. Duration of an output frame: Since the frame rate is 50,000 frames per second, the duration of each frame is 1/50,000 of a second, or 20 microseconds.
4. Output data rate: The output data rate would be the frame rate multiplied by the number of bits per frame. That's 50,000 frames/second multiplied by 41 bits/frame, which equals 2,050,000 bps (or 2.05 Mbps).
5. Efficiency of the system: The ratio of useful bits (the original data) to total bits in the frame can be calculated. There are 40 useful bits and 41 total bits per frame, hence the efficiency is 40/41, or approximately 97.56%.