Question

How "wide" is a bit on a 1-Gbps link? How long is a bit in copper wire, where the speed of propagation is \(2.3 \times 10^{8} \mathrm{~m} / \mathrm{s}\) ?

Short answer

0.23 meters.

Step-by-step solution

- Understand the Problem

Determine how long a single bit takes to travel on a 1-Gbps link with a propagation speed of \(2.3 \times 10^8 \text{ meters/second}\).

- Calculate Bit Time

The bit rate is 1 Gbps (\(10^9 \text{ bits/second}\)). Therefore, the time to transmit one bit is the inverse of the bit rate: \[ \text{Bit Time} = \frac{1}{\text{Bit Rate}} = \frac{1}{10^9 \text{ bits/second}} \].

- Time Calculation

Solving the above equation: \[ \text{Bit Time} = 10^{-9} \text{ seconds (or nanoseconds)} \].

- Calculate Bit Length

To find the length of a bit in the wire, multiply the propagation speed by the bit time: \[ \text{Bit Length} = \text{Propagation Speed} \times \text{Bit Time} \].

- Length Calculation

Using the given propagation speed \(2.3 \times 10^8 \text{ meters/second}\) and bit time \(10^{-9} \text{ seconds}\): \[ \text{Bit Length} = 2.3 \times 10^8 \text{ meters/second} \times 10^{-9} \text{ seconds} \]. This simplifies to: \[ \text{Bit Length} = 0.23 \text{ meters} \].

Key concepts

bit rate

Bit rate is the number of bits transmitted per second in a communication channel. In this exercise, we deal with a 1-Gbps (Gigabit per second) link. This means that the channel transmits 1 billion bits every second. Understanding bit rate is vital because it directly influences how much data can be transferred in a given time frame. The formula for bit rate is simple: it's the total number of bits divided by the time in seconds. So, for our 1-Gbps link, the bit rate is:

• 1 Gbps = \(1 \times 10^9\) bits per second.

Knowing the bit rate helps in determining other key parameters, such as bit time, which is critical for calculating how

propagation speed

Propagation speed refers to the speed at which a signal travels through a medium, such as copper wire or fiber optic cable. In the context of this exercise, the propagation speed is given as \(2.3 \times 10^8\) meters per second. This is the speed at which an electrical signal moves through the copper wire. To put it into perspective, light travels at a speed of approximately \(3 \times 10^8\) meters per second, so our signal is traveling at a speed that is quite fast but somewhat slower than light. Understanding propagation speed is crucial for calculating how long it takes for a signal to travel a certain distance. It helps in determining the bit length, which is the physical distance a single bit occupies in the medium.

bit time

Bit time is the duration it takes for one bit to be transmitted and it can be calculated using the bit rate. For a 1-Gbps link, the bit time is the inverse of the bit rate. The formula used is:

• \text{Bit Time} = \frac{1}{\text{Bit Rate}}

In our exercise, the bit rate is 1 Gbps (\(10^9\) bits per second), so the bit time is:

• \text{Bit Time} = \frac{1}{10^9 \text{ bits/second}} = 10^{-9}$ or 1 nanosecond.

To determine how