Respuesta :
Answer:
The total time elapsed from the time a bit is created (from the original analog signal at Host A) until the bit is decoded (as part of the analog signal at Host B is 25.11 ms
Explanation:
Host A first converts the analog signal to a digital 64kbps stream and then groups it into 56-byte packets. The time taken for this can be calculated as:
time taken 1= [tex]\frac{Packet Size in Bits}{Bit Rate}[/tex]
= (56 x 8) bits / 64 x 10³ bits/s
= 7 x 10⁻³s
time taken 1= 7 ms
The transmission rate of the packet from Host A to Host B is 4 Mbps. The time taken to transfer the packets can be calculated as:
time taken 2= (56 x 8) bits / 4 x 10⁶ bits/s
= 1.12 x 10⁻⁴ s
time taken 2= 112 μs
The propagation delay is 18 ms.
To calculate the total time elapsed, we need to add up all the time taken at each individual stage.
[tex]Time_{total}[/tex] = Time taken 1 + Time taken 2 + Propagation Delay
= 7 ms + 112 μs + 18 ms
= 0.025112 s
[tex]Time_{total}[/tex] = 25.11 ms
Therefore, the time elapsed from the time a bit is created until the bit is decoded at Host B is 0.009896 sec or 9.986 msec.
It is given that,
Host A converts the analog signal to digital bit stream = 64kbps =64 x 103 bps [ 1 kbps=103 bps]
The size of the packet of converted bits = 56 bytes = 56 x 8 bits [1 byte= 8 bits]
Transmission rate of link between Host A and Host B=500 kbps = 500 x 103 bps [1kbps = 103 bps]
Propagation delay= 2 msec. or 0.002sec. [1 msec=1/1000 sec]
Consider the first bit of the packet.
Host A converts an analog signal into digital bit stream. Thus, first bit in the packet must wait until all the bits in the packet are generated.
The time required to generate all the bits in the packet
[tex]\frac{56\times8}{64\times10^3} =0.007 sec[/tex]
The time required to transmit the packet (all bits) into link (or transmission delay)
[tex]\frac{56\times}{2\times10^6} =0.000896 sec[/tex]
It is already given that the propagation delay=2 msec or 0.002 sec. That is, each bit takes 2 msec. to travel from starting of the link to Host B.
The time elapses between the creation and decoding of a bit is the sum of time required for converting analog signal to digital bit stream, transmission delay and propagation delay.
Thus, the time elapses between the creation and decoding of a bit
=Time required for conversion + transmission delay + propagation delay.
= 0.007 + 0.000896 + 0.002 sec
=0.009896 sec
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