What is the minimum frame size for a CSMA/CD network running at 1 Gbps over a 1-km cable with a signal speed of 200,000 km/sec?
The minimum frame size for a CSMA/CD network running at 1 Gbps over a 1-km cable with a signal speed of 200,000 km/sec is 1250 bytes. This calculation involves determining the round-trip signal travel time and then multiplying by the network speed to find the minimum bits required, which are then converted into bytes.
Understanding Minimum Frame Size Calculation
CSMA/CD Network: The Carrier Sense Multiple Access with Collision Detection (CSMA/CD) network protocol is used to manage access to the shared transmission medium within Ethernet networks.
Calculating Round-Trip Signal Travel Time
To calculate the minimum frame size for a CSMA/CD network, we first need to determine the round-trip time it takes for a signal to be detected as a collision. This time depends on the cable length and the signal speed within the cable.
1. Convert Cable Length: The 1-km cable is converted to meters, where 1 km equals 1000 meters.
2. Calculate Signal Travel Time: The signal travel time for one-way transmission is calculated by dividing the cable length by the signal speed: (1000 m) / (200,000 km/s) = 5 × 10-6 seconds.
3. Determine Round-Trip Time: The round-trip travel time is twice the one-way time: 5 × 10-6 seconds × 2 = 10 × 10-6 seconds = 10 microseconds.
Finding Minimum Frame Size
Next, we calculate the minimum frame size that can occupy the network for the determined round-trip time, considering the network speed of 1 Gbps (1 Gigabit per second).
1. Multiply Round-Trip Time by Network Speed: Multiply the round-trip time by the network speed to find the minimum bits required: 10 × 10-6 seconds × 10^9 bits per second = 104 bits.
2. Convert Bits to Bytes: As a byte consists of 8 bits, we convert the minimum frame size to the nearest whole byte: 104 bits / 8 = 1250 bytes.
Therefore, the minimum frame size for a CSMA/CD network running at 1 Gbps over a 1-km cable with a signal speed of 200,000 km/sec is 1250 bytes.