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Transmission units and calculations

Network questions often combine a file size in bytes with a transmission rate in bits per second. Successful calculations begin by making the units compatible, then applying the relationship between file size, rate and time.

1. Make units compatible

Use these facts when the question supplies these units:

1 byte = 8 bits
network rate: 1 kbit/s = 1000 bit/s, 1 Mbit/s = 1000² bit/s, 1 Gbit/s = 1000³ bit/s
binary file units: 1 KiB = 1024 bytes, 1 MiB = 1024² bytes, 1 GiB = 1024³ bytes

Read the unit printed in the question. Do not silently replace 1000 with 1024 or treat bytes and bits as interchangeable.

Fill in the blanks3 marks

One byte contains gap 1 bits. A network rate of one Mbit/s is gap 2 bits per second. One MiB contains gap 3 bytes.

8
1000
1000²
1024
1024²

Multiple choice1 mark

A file contains 6000 bytes. How many bits does it contain?

A750 bits
B6000 bits
C6 000 000 bits
D48 000 bits

2. Choose the relationship

The three quantities are linked:

time (seconds) = file size (bits) / rate (bits per second)

file size (bits) = rate (bits per second) × time (seconds)

rate (bits per second) = file size (bits) / time (seconds)

Units are part of the method. Dividing bits by bits per second leaves seconds.

Written answer2 marks

A 24 000 bit file is sent at 6000 bit/s. Calculate the transmission time.

Show the expression, value and unit.

Students type their answer here.

Multiple choice1 mark

Which expression calculates the number of bits sent in 35 seconds at 2 Mbit/s?

A`2 × 1000² × 35`
B`2 × 1024² / 35`
C`35 / (2 × 8)`
D`2 × 8 × 35`

3. Model a mixed-unit expression

A 1.5 MiB file is transmitted at 6 Mbit/s.

Convert the file to bytes: 1.5 × 1024².
Convert bytes to bits: 1.5 × 1024² × 8.
Convert the rate to bit/s: 6 × 1000².
Divide size by rate:

time = (1.5 × 1024² × 8) / (6 × 1000²)

The expression is often the important examination evidence because it shows every required conversion.

Written answer4 marks

Construct an expression for the time needed to transmit a 2.4 MiB file at 8 Mbit/s. You do not need to evaluate it.

Show binary file conversion, byte-to-bit conversion and decimal rate conversion.

Students type their answer here.

4. Match time units too

A rate in bits per second requires time in seconds. Convert minutes using minutes × 60. Convert hours using hours × 60 × 60.

Model: Data sent in 3 minutes at 5 Mbit/s is 5 × 1000² × (3 × 60) bits.

Written answer2 marks

Construct an expression for the number of bits transmitted in 12 minutes at 40 Mbit/s.

Convert both the rate and the time before multiplying.

Students type their answer here.

Multiple choice1 mark

A student calculates (3 × 1024²) / (12 × 1000²) for a 3 MiB file sent at 12 Mbit/s. Which conversion is missing?

Aseconds to minutes
Bmetres to kilometres
Cbytes to bits
Ddecimal to hexadecimal

Written answer3 marks

Calculate the time for an 8 MB file to transmit at 16 Mbit/s, using 1 MB = 1000² bytes for this question.

Convert the file to bits, then divide by the rate. Show units.

Students type their answer here.

Written answer2 marks

Explain why using 1024² for every Mbit/s conversion can produce a wrong answer.

Distinguish SI transmission prefixes from IEC binary file units.

Students type their answer here.

Multiple choice1 mark

Which checklist is correct before calculating transmission time?

AAlways multiply every number by 1024.
BConvert size and rate to compatible bit units, convert time units if needed, then divide size by rate.
CDivide rate by file size and ignore units.
DConvert bits to metres before dividing.

Route forward

You can construct and evaluate transmission expressions without mixing bits, bytes, SI and binary multipliers. Next you will compare the physical and wireless media that carry network data.