Hardware, Memory & Number Systems

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Memory units and conversions

⏱ 5 min read🧩 5 question types🎯 16 practice Q

The idea in one minute

Data is stored as bits. Eight bits make one byte. Each unit above the byte is 1024 times the one below it. File sizes use bytes (MB, GB). Internet speeds use bits (Mbps). Exams always test this difference.

The unit ladder

The smallest unit is the bit. It is one 0 or one 1. Above the byte, every step multiplies by 1024, which is $2^{10}$ .

Unit	Equals
1 Nibble	4 bits
1 Byte (B)	8 bits
1 KiloByte (KB)	1024 B
1 MegaByte (MB)	1024 KB
1 GigaByte (GB)	1024 MB
1 TeraByte (TB)	1024 GB
1 PetaByte (PB)	1024 TB

Rule: Exams use 1024, never 1000.

Some exact values to remember. 1 MB is $2^{20}$ = 10,48,576 bytes. 1 GB is $2^{30}$ = 1,07,37,41,824 bytes.

How to convert

Going up the ladder, divide by 1024. Going down, multiply by 1024.

4 GB to MB: 4 × 1024 = 4096 MB.
2048 KB to MB: 2048 ÷ 1024 = 2 MB.
Bits in 2 KB: 2 × 1024 = 2048 bytes. Then 2048 × 8 = 16,384 bits.

Tip: For "which is largest", change every option to the same unit first. KB is usually easiest.

Bits and bytes in speed questions

File sizes and storage are measured in bytes (MB, GB). Line speeds are measured in bits. Mbps means megabits per second.

Eight bits make one byte. So an 8 Mbps line moves about 1 MB of file data each second.

Watch: Capital B is a byte. Small b is a bit. Mb is a megabit. MB is a megabyte.

Try a quick one. A plan says 24 Mbps. Divide by 8. You get 3 MB per second. A 30 MB file then needs 10 seconds. Always divide the size in MB by the speed in MB per second.

Download time in three steps

Take a 10 MB file on a 16 Mbps line.

Change the file to bits. 10 × 8 = 80 megabits.
Divide by the speed. 80 ÷ 16 = 5.
The answer is 5 seconds.

You can also change the speed to bytes. 16 ÷ 8 = 2 MB per second. Then 10 ÷ 2 = 5 seconds.

Which option is largest

Take the options 1024 KB, 1 MB, 10,00,000 bytes and 0.5 GB. Put everything in KB.

Option	In KB
1024 KB	1024
1 MB	1024
10,00,000 bytes	about 977
0.5 GB	5,24,288

So 0.5 GB is the largest.

Other units you may meet

Word length is the number of bits a CPU handles in one go. A 64-bit processor has a 64-bit word.
The smallest unit of data is the bit.
The smallest unit of memory usually addressed is 1 byte.
Half a byte is a nibble (4 bits). One hexadecimal digit is exactly one nibble.

Everyday sizes

Use these to reject silly options fast.

A phone photo is about 2 to 5 MB.
A movie is about 1 to 4 GB.
A good laptop SSD is about 512 GB to 1 TB.
Internet plans are sold in Mbps. Your browser shows MB per second. An 80 Mbps line downloads near 10 MB per second.

Question types you will see

Each type: how to recognise it, the method step by step, and one question to try.

Type 1very common3 practice Q

Bit, nibble and byte definitions

How to spot it:

'How many bits in...', 'nibble' or 'smallest unit'.

Method

Remember: 1 byte = 8 bits and 1 nibble = 4 bits.
So one byte is two nibbles.
For bigger counts, multiply. Bits = bytes × 8.
One hex digit equals one nibble.

Why it works:

Every larger unit is built from the byte.

Try this

How many bits are there in 3 bytes?

Show solution

Each byte has 8 bits.
3 × 8 = 24.

Answer

24 bits

Type 2very common6 practice Q

KB, MB, GB, TB ladder conversion

How to spot it:

'How many MB in 4 GB', 'convert KB to MB' or 'which is largest'.

Method

Decide: are you going up or down the ladder?
Down: multiply by 1024. Up: divide by 1024.
Do it one rung at a time.
For 'largest', change all options to one unit.

Why it works:

Every rung of the ladder is the same factor, 1024.

Try this

A pen drive holds 4 GB. How many MB is that (exam convention)?

Show solution

GB to MB goes down one rung.
4 × 1024 = 4096.

Answer

4096 MB

Type 3common3 practice Q

Bits vs bytes in data-transfer speed

How to spot it:

'Mbps', 'download time', 'per second' or 'speed of the line'.

Method

Check the units: Mb or MB?
Change the file to bits (× 8), or the speed to bytes (÷ 8).
Divide file size by speed, in the same unit.
8 Mbps equals 1 MB per second.

Why it works:

Speed is measured in bits but files are measured in bytes.

Try this

A connection delivers 16 Mbps. How many megabytes is that per second?

Show solution

Eight bits make one byte.
So divide 16 by 8.

Answer

2 MB per second

Type 4common3 practice Q

Unit odd-one-out and definitions

How to spot it:

'Which is NOT a unit of data size' or 'word length'.

Method

Size units: bit, nibble, byte, KB, MB, GB, TB, PB.
Mbps is a speed unit, not a size unit.
Word length is the bits a CPU processes in one operation.
Cross out the speed unit.

Why it works:

Odd-one-out questions usually hide a speed unit among size units.

Try this

Which of the following is NOT a unit of data size? KB, MB, Mbps, GB

Show solution

KB, MB and GB measure size.
Mbps is megabits per second, a speed.

Answer

Mbps

Type 5common

Download time and bit counts

How to spot it:

'How long to download', 'how many bits in 2 KB' or 'time for a file'.

Method

Write the file size in one unit.
Change bytes to bits with × 8.
Divide bits by the line speed in bits per second.
Check that the units cancel.

Why it works:

Time is size divided by speed, so both must use bits.

Try this

How long will a 10 MB file take on a 16 Mbps line?

Show solution

10 MB = 10 × 8 = 80 megabits.
80 ÷ 16 = 5.

Answer

5 seconds

Formula sheet

Step multiplier

1\ \text{unit}_{next} = 2^{10} = 1024\ \text{units}_{prev}

KB->MB->GB->TB->PB all multiply by 1024

Byte identity

1\ \text{Byte} = 8\ \text{bits},\quad 1\ \text{Nibble} = 4\ \text{bits}

half a byte = nibble

Common ladders

1\ \text{GB} = 1024\ \text{MB} = 2^{20}\ \text{KB} = 2^{30}\ \text{B}

4 GB = 4096 MB = 2^22 KB

bits vs bytes

1\ \text{MB} = 8\ \text{Mb}

capital B = byte, small b = bit (speeds are usually bits)

Shortcuts that save time

⚡ The 1024 ladder

Every step up multiplies by 1024 ( $2^{10}$ ), never 1000. Half a KB is 512 B.

Example

2 GB = ? KB

Show solution

2 GB = 2 × 1024 MB = 2048 MB.
2048 MB × 1024 = 20,97,152 KB.

Answer

20,97,152 KB (which is $2^{21}$ )

⚡ Bit or byte speed check

Line speeds are in bits (Mbps). File sizes are in bytes (MB). To get MB per second, divide Mbps by 8.

Example

A 16 Mbps line moves how many MB per second?

Show solution

Divide the bits by 8.
16 ÷ 8 = 2.

Answer

2 MB per second

Mistakes to avoid

Where most students lose marks on this subtopic.

Mistake 01

Using 1000 instead of 1024 in a ladder question.

Exams use 1024 at every step.

Mistake 02

Reading Mbps as megabytes per second.

Mbps is megabits. Divide by 8 to get MB per second.

Mistake 03

Multiplying by 1024 when going up the ladder.

Going up (KB to MB) divides by 1024. Going down multiplies.

Mistake 04

Forgetting to multiply by 8 when a question asks for bits.

Bytes to bits is always × 8.

Mistake 05

Comparing options in different units.

Convert all options to one unit before comparing.

Quick revision

Read this the night before the exam.

Bit, Nibble (4 bits), Byte (8 bits), KB, MB, GB, TB, PB. Each step is × 1024.
4 GB = 4096 MB. 2048 KB = 2 MB. 1 TB = 1024 GB.
Speeds are in bits. 8 Mbps is about 1 MB per second of file data.
Nibble = 4 bits = one hex digit. Smallest unit is the bit.
Word length is the bits a CPU handles at once.

Practice: 16 questions

Sets of 10, mixed across the question types above. Every answer has a step-by-step explanation.

Topic test · 10 questions

Suggested time 4 min · wrong answers go to your mistake notebook automatically.

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