What is the bit rate for each of the following signal?
a. A signal in which a bit lasts 0.001 s
b. A signal in which a bit lasts 2 ms
c. A signal in which 10 bit lasts 20µ s
d. A signal in which 1000 bits lasts 250 ps
The correct answer and explanation is :
Bit Rate Calculation
Bit rate refers to the number of bits transmitted per unit of time, typically expressed in bits per second (bps). The formula to calculate the bit rate is:
[
\text{Bit rate} = \frac{1}{\text{Time per bit}}
]
Where:
- Time per bit is the duration for one bit to be transmitted.
- The result will give us the number of bits transmitted in one second (bit rate).
Let’s calculate the bit rate for each case:
a. A signal in which a bit lasts 0.001 s
- Time per bit = 0.001 seconds.
Using the formula:
[
\text{Bit rate} = \frac{1}{0.001} = 1000 \, \text{bps}
]
So, the bit rate is 1000 bps.
b. A signal in which a bit lasts 2 ms
- Time per bit = 2 milliseconds = 0.002 seconds.
Using the formula:
[
\text{Bit rate} = \frac{1}{0.002} = 500 \, \text{bps}
]
So, the bit rate is 500 bps.
c. A signal in which 10 bits lasts 20 µs
- Time for 10 bits = 20 microseconds = ( 20 \times 10^{-6} ) seconds.
The time per bit would be:
[
\text{Time per bit} = \frac{20 \times 10^{-6}}{10} = 2 \times 10^{-6} \, \text{seconds}
]
Now, the bit rate is:
[
\text{Bit rate} = \frac{1}{2 \times 10^{-6}} = 500,000 \, \text{bps}
]
So, the bit rate is 500,000 bps.
d. A signal in which 1000 bits lasts 250 ps
- Time for 1000 bits = 250 picoseconds = ( 250 \times 10^{-12} ) seconds.
The time per bit is:
[
\text{Time per bit} = \frac{250 \times 10^{-12}}{1000} = 250 \times 10^{-15} \, \text{seconds}
]
Now, the bit rate is:
[
\text{Bit rate} = \frac{1}{250 \times 10^{-15}} = 4 \times 10^{12} \, \text{bps} = 4 \, \text{Tbps}
]
So, the bit rate is 4 Tbps.
Explanation
The bit rate is determined by how quickly bits can be transmitted. The shorter the duration of a bit, the higher the bit rate. For instance, in part (a), the bit rate is higher because the time per bit is shorter (0.001 seconds per bit). In contrast, in part (d), even though there are 1000 bits, the time span is extremely small (250 picoseconds), resulting in an exceptionally high bit rate (4 terabits per second).