Hardware, Memory & Number Systems
🔒 Log in to trackMemory units and conversions
🔒 Log in to trackThe ladder (exam convention: each step is x1024):
| Unit | Equals | Value in bytes |
|---|---|---|
| 1 bit | smallest unit (0 or 1) | - |
| 1 Nibble | 4 bits | - |
| 1 Byte | 8 bits | 1 |
| 1 KiloByte (KB) | 1024 B | 2^10 |
| 1 MegaByte (MB) | 1024 KB | 2^20 = 1,048,576 B |
| 1 GigaByte (GB) | 1024 MB | 2^30 = 1,07,37,41,824 B |
| 1 TeraByte (TB) | 1024 GB | 2^40 |
| 1 PetaByte (PB) | 1024 TB | 2^50 |
| 1 ExaByte (EB) | 1024 PB | 2^60 |
A word is the number of bits a CPU handles at once (16/32/64-bit). Careful: lowercase b = bit, uppercase B = byte - 1 Mbps (megabit/s) = 0.125 MB/s. (Purists use KiB/MiB for the 1024-based values; SSC uses the KB = 1024 B convention.)
The unit ladder
All data is stored as bits. The units stack up by 1024 (2 to the power 10) at each step — exam convention, never 1000:
| Unit | Equals | In bytes |
|---|---|---|
| 1 bit | smallest unit — one 0 or 1 | — |
| 1 Nibble | 4 bits | — |
| 1 Byte (B) | 8 bits | 1 |
| 1 KiloByte (KB) | 1024 B | 2¹⁰ |
| 1 MegaByte (MB) | 1024 KB | 2²⁰ = 10,48,576 B |
| 1 GigaByte (GB) | 1024 MB | 2³⁰ = 1,07,37,41,824 B |
| 1 TeraByte (TB) | 1024 GB | 2⁴⁰ |
| 1 PetaByte (PB) | 1024 TB | 2⁵⁰ |
How to convert: going up → divide by 1024 at each step; going down → multiply by 1024. Example: 4 GB = 4 × 1024 = 4096 MB; 2048 KB = 2048 ÷ 1024 = 2 MB.
Other asked units
- Word length — the number of bits a CPU handles in one go (a '64-bit processor').
- Smallest unit of data = bit; smallest unit of memory addressable = usually 1 byte.
- Half a byte (4 bits) = nibble — one hexadecimal digit is exactly one nibble.
Worked examples in exam style
- 4 GB to MB: climb down one rung — 4 × 1024 = 4096 MB.
- 2048 KB to MB: climb up — 2048 ÷ 1024 = 2 MB.
- Bits in 2 KB: 2 × 1024 = 2048 bytes, then × 8 = 16,384 bits.
- Download time: a 10 MB file on a 16 Mbps line: file = 10 × 8 = 80 megabits; 80 ÷ 16 = 5 seconds.
- Which is largest among 1024 KB, 1 MB, 10,00,000 bytes, 0.5 GB: put everything in KB — 1024, 1024, about 977, 5,24,288 → 0.5 GB wins.
Where you already use this ladder
- Internet plans are sold in Mbps (bits), but your browser shows MB/s (bytes) — an 80 Mbps line downloads near 10 MB/s.
- A phone photo ≈ 2–5 MB, a movie ≈ 1–4 GB, a good laptop SSD ≈ 512 GB–1 TB. These everyday anchors help you reject absurd options instantly.
Question types you will see
Each type: how to recognise it, the method step by step, and one question to try.
Bit / nibble / byte definitions
'How many bits in a byte/nibble?', 'how many nibbles in a byte?', 'bits in 3 bytes?' — direct small-number questions.
Fixed facts: 1 byte = 8 bits, 1 nibble = 4 bits, so a byte = 2 nibbles.
Multiply for bigger counts: 3 bytes = 3 × 8 = 24 bits.
One hex digit = one nibble — a free link to hexadecimal questions.
How many bits are there in 3 bytes?
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3 × 8 = 24 bits — one byte always carries exactly 8 bits.
KB → MB → GB → TB ladder conversion
'4 GB = how many MB?', '2 TB = how many GB?', 'which is largest', 'a folder of n files of 512 KB is how many MB'.
Every step is ×1024 going up, ÷1024 going down — never 1000.
4 GB = 4 × 1024 = 4096 MB; 2048 KB = 2 MB; 1 TB = 1024 GB.
For 'which is largest', convert everything to one unit (say KB) before comparing.
A pen drive holds 4 GB. How many MB is that (exam convention)?
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4 × 1024 = 4096 MB. Each step up the ladder multiplies by 1024, so going from GB to MB multiplies by 1024.
Bits vs bytes in data-transfer speed
'A 16 Mbps line downloads a 10 MB file in how long?', '8 Mbps equals how many MB/s?' — speed given in megabits, file in megabytes.
Convert the file to bits (×8) or the speed to bytes (÷8) before dividing.
8 Mbps = 1 MB/s; 16 Mbps = 2 MB/s.
Time = file size ÷ effective speed, both in the same unit.
A connection delivers 16 Mbps (megabits per second). How many megabytes is that per second?
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16 ÷ 8 = 2 MB per second — eight bits make one byte, so divide the bit-rate by 8.
Unit odd-one-out and definitions
'The smallest unit of data is', 'word length means', 'which is not a unit of memory'.
Bit = smallest unit; byte = 8 bits; nibble = 4 bits.
Word length = bits the CPU processes in one operation (hence '64-bit processor').
Odd-one-out versions usually slip in a speed unit (Mbps) among size units (KB, MB, GB).
Which of the following is NOT a unit of data size?
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Mbps — megabits per second, a speed unit. KB, MB and GB measure size.
Formula sheet
KB->MB->GB->TB->PB all multiply by 1024
half a byte = nibble
4 GB = 4096 MB = 2^22 KB
capital B = byte, small b = bit (speeds are usually bits)
Shortcuts that save time
Every step up multiplies by 1024 (2^10), never 1000 in SSC convention. 4 GB = 4 x 1024 = 4096 MB. Half a KB = 512 B.
2 GB = ? KB
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2 x 1024 x 1024 = 2^21 = 2,048 KB x 1024 = 20,97,152 KB - or 2^21 KB.
Line speeds are in bits (Mbps), file sizes in bytes (MB). To convert a download speed to MB/s, divide by 8: 8 Mbps = 1 MB/s.
16 Mbps line - max MB downloaded per second?
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16/8 = 2 MB per second.
Mistakes to avoid
Where most students lose marks on this subtopic.
Using 1000 instead of 1024 for unit steps in exam questions.
Confusing Mb (megabit) with MB (megabyte) in speed questions.
Saying a nibble is 8 bits - a nibble is 4 bits (half a byte).
Quick revision
Read this the night before the exam.
Bit → Nibble (4) → Byte (8) → KB (1024) → MB → GB → TB → PB; each step ×1024.
4 GB = 4096 MB; 2048 KB = 2 MB; 1 TB = 1024 GB.
Speeds are in bits: 8 Mbps ≈ 1 MB/s of file data.
Nibble = 4 bits = one hex digit. Smallest unit = bit.
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.