4.1.5 - Transmission calculations

Network-speed units

A network transmission rate tells you how many bits can be transferred each second. A rate of 60 Mbps therefore describes a flow of bits, not a file size.

Pearson uses decimal SI multiples for network rates. Each step in this table is 1000 times the previous unit.

The order is:

bps < kbps < Mbps < Gbps

To convert to a smaller unit, multiply by 1000 for each step. To convert to a larger unit, divide by 1000 for each step.

For example:

2.5 Gbps = 2.5 x 1000 = 2500 Mbps

2500 Mbps = 2500 x 1000 = 2,500,000 kbps

The letter case matters:

• lowercase b means bit;
• uppercase B means byte;
• 1 B = 8 bits.

So Mb is an amount of data in megabits, while Mbps is a rate in megabits per second.

Three linked quantities

Every transmission expression links three quantities:

When the units are compatible, the basic relationship is:

S = R x T

Rearranging it gives all three useful expressions:

The unit check is more reliable than choosing an operation from memory. If the units do not cancel to the unit requested, either the expression or a conversion is wrong.

For example, a 40,000,000-bit file sent at 10,000,000 bits/s takes:

T = 40,000,000 bits / 10,000,000 bits/s = 4 s

The bits cancel, leaving seconds. Also notice the direction of the relationship: for the same file size, a larger rate gives a shorter time because the rate is the divisor.

Finding transmission time

To find a transmission time, divide the file size in bits by the rate in bits per second.

Worked example: compatible decimal units

A file contains 96,000,000 bits. It is transmitted at 12 Mbps. Calculate the transmission time.

First convert the rate:

12 Mbps = 12 x 1,000,000 = 12,000,000 bits/s

Now divide file size by rate:

T = 96,000,000 bits / 12,000,000 bits/s

T = 8 s

The final unit is seconds because the rate was per second.

When a file size is given in MiB

Network rates use decimal multiples, but a file size may use a binary multiple:

The i in MiB is the clue that the multiplier is 1024, and the uppercase B shows bytes. By contrast, Mbps has no i, uses a multiplier of 1000 for each prefix step, and its lowercase b means bits.

Suppose a 14 MiB file is transmitted at 7 Mbps. Convert each quantity inside the expression: