Fórmulas Primer parcial (Teoría de las Comunicaciones)

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Bandwidth and latency

• Latency = Propagation + Transmit + Queue
• Propagation = Distance/SpeedOfMedium
• Transmit = Size/Bandwidth

Shannon's Theorem

$C=B\times log_{2}(1+S/N)$

• B es el ancho de banda
• C es la capacidad
• S/N es la relacion señal ruido en dB

Subnetting

Applying a subnet mask to an IP address allows you to identify the network and node parts of the address. The network bits are represented by the 1s in the mask, and the node bits are represented by the 0s. Performing a bitwise logical AND operation between the IP address and the subnet mask results in the Network Address or Number.

For example, using our test IP address and the default Class B subnet mask, we get:

10001100.10110011.11110000.11001000      140.179.240.200   IP Address
11111111.11111111.00000000.00000000      255.255.000.000   Default Subnet Mask
--------------------------------------------------------
10001100.10110011.00000000.00000000      140.179.000.000   Network Address

To calculate the number of subnets or nodes, use the formula ($2^{n}-2$) where n = number of bits in either field, and $2^{n}$ represents 2 raised to the nth power. Multiplying the number of subnets by the number of nodes available per subnet gives you the total number of nodes available for your class and subnet mask. Also, note that although subnet masks with non-contiguous mask bits are allowed, they are not recommended.

Example:

10001100.10110011.11011100.11001000      140.179.220.200   IP Address
11111111.11111111.11100000.00000000      255.255.224.000   Subnet Mask
--------------------------------------------------------
10001100.10110011.11000000.00000000      140.179.192.000   Subnet Address
10001100.10110011.11011111.11111111      140.179.223.255   Broadcast Address

In this example a 3 bit subnet mask was used. There are 6 ($2^{3}-2$) subnets available with this size mask (remember that subnets with all 0's and all 1's are not allowed). Each subnet has 8190 ($2^{13}-2$) nodes. Each subnet can have nodes assigned to any address between the Subnet address and the Broadcast address. This gives a total of 49,140 nodes for the entire class B address subnetted this way.

You can calculate the Subnet Address by performing a bitwise logical AND operation between the IP address and the subnet mask, then setting all the host bits to 0s. Similarly, you can calculate the Broadcast Address for a subnet by performing the same logical AND between the IP address and the subnet mask, then setting all the host bits to 1s. That is how these numbers are derived in the example above.