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 :
Explanation of Bit Rate Calculation:
Bit rate refers to the number of bits transmitted per second, and it is typically measured in bits per second (bps). The bit rate can be calculated as the inverse of the duration of a bit. Specifically:
[
\text{Bit Rate (bps)} = \frac{1}{\text{Bit Duration (seconds)}}
]
If we are given the duration of one bit, we can easily compute the bit rate. For cases where we are given the total duration for multiple bits, we simply divide the total number of bits by the total duration.
Now, let’s calculate the bit rate for each case:
a. A signal in which a bit lasts 0.001 s
Given that the duration of one bit is 0.001 seconds, the bit rate is:
[
\text{Bit Rate} = \frac{1}{0.001 \text{ seconds}} = 1000 \text{ bps}
]
So, the bit rate for this signal is 1000 bps.
b. A signal in which a bit lasts 2 ms
Here, the duration of one bit is 2 milliseconds (ms), which is equivalent to 2 × 10⁻³ seconds. Therefore, the bit rate is:
[
\text{Bit Rate} = \frac{1}{2 \times 10^{-3} \text{ seconds}} = 500 \text{ bps}
]
Thus, the bit rate for this signal is 500 bps.
c. A signal in which 10 bits lasts 20 µs
Here, the total duration for 10 bits is 20 microseconds (µs), which is 20 × 10⁻⁶ seconds. To find the bit duration, we divide the total duration by the number of bits:
[
\text{Bit Duration} = \frac{20 \times 10^{-6} \text{ seconds}}{10} = 2 \times 10^{-6} \text{ seconds}
]
Now, the bit rate is the inverse of the bit duration:
[
\text{Bit Rate} = \frac{1}{2 \times 10^{-6} \text{ seconds}} = 500,000 \text{ bps}
]
Thus, the bit rate for this signal is 500,000 bps or 500 kbps.
d. A signal in which 1000 bits lasts 250 ps
In this case, the total duration for 1000 bits is 250 picoseconds (ps), which is equivalent to 250 × 10⁻¹² seconds. To find the bit duration, we divide the total duration by the number of bits:
[
\text{Bit Duration} = \frac{250 \times 10^{-12} \text{ seconds}}{1000} = 250 \times 10^{-15} \text{ seconds}
]
The bit rate is the inverse of the bit duration:
[
\text{Bit Rate} = \frac{1}{250 \times 10^{-15} \text{ seconds}} = 4 \times 10^{12} \text{ bps} = 4 \text{ Tbps}
]
Thus, the bit rate for this signal is 4 Tbps.
Summary of Results:
- a: 1000 bps
- b: 500 bps
- c: 500,000 bps (500 kbps)
- d: 4 Tbps
These calculations show how the bit rate is directly tied to the duration of each bit, and it illustrates how fast data can be transmitted depending on how short the bit duration is. The shorter the bit duration, the higher the bit rate.