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 :
To determine the bit rate for each signal, we use the formula:
[
\text{Bit Rate (in bits per second)} = \frac{1}{\text{Time per bit (in seconds)}}
]
The bit rate tells us how many bits are transmitted per second. The time per bit is the duration that one bit takes to be transmitted.
a. A signal in which a bit lasts 0.001 s
In this case, the time per bit is given as 0.001 seconds.
[
\text{Bit Rate} = \frac{1}{0.001} = 1000 \text{ bits per second (bps)}
]
So, the bit rate is 1000 bps.
b. A signal in which a bit lasts 2 ms
Here, the time per bit is 2 milliseconds (ms). To convert milliseconds to seconds, we divide by 1000:
[
2 \text{ ms} = 2 \times 10^{-3} \text{ seconds}
]
Now, using the bit rate formula:
[
\text{Bit Rate} = \frac{1}{2 \times 10^{-3}} = 500 \text{ bps}
]
So, the bit rate is 500 bps.
c. A signal in which 10 bits lasts 20 µs
In this case, the duration for 10 bits is given as 20 microseconds (µs). First, convert microseconds to seconds:
[
20 \text{ µs} = 20 \times 10^{-6} \text{ seconds}
]
Now, the time for one bit is:
[
\text{Time per bit} = \frac{20 \times 10^{-6}}{10} = 2 \times 10^{-6} \text{ seconds}
]
Then, calculate the bit rate:
[
\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
Here, the duration for 1000 bits is given as 250 picoseconds (ps). First, convert picoseconds to seconds:
[
250 \text{ ps} = 250 \times 10^{-12} \text{ seconds}
]
Now, the time for one bit is:
[
\text{Time per bit} = \frac{250 \times 10^{-12}}{1000} = 250 \times 10^{-15} \text{ seconds}
]
Then, calculate the bit rate:
[
\text{Bit Rate} = \frac{1}{250 \times 10^{-15}} = 4 \times 10^{12} \text{ bps}
]
So, the bit rate is 4 terabits per second (4 Tbps).
Summary of the bit rates:
- a. 1000 bps
- b. 500 bps
- c. 500,000 bps
- d. 4 Tbps
The calculation for each case follows the basic principle that the bit rate is the reciprocal of the time taken to transmit a single bit. The smaller the time per bit, the higher the bit rate, leading to faster data transmission.