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.)
Detailed notes
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.
Bits vs bytes — the speed trap
- File sizes and storage are measured in bytes (MB, GB).
- Line speeds are measured in bits: Mbps = megaBITS per second.
- 8 bits = 1 byte, so an 8 Mbps line moves about 1 MB of file data per second. A 16 Mbps connection downloads a 10 MB file in about 10 × 8 ÷ 16 = 5 seconds. Watch the case: Mb = megabit, MB = megabyte.
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.
Two traps that decide the mark
- Using 1000 instead of 1024 — every ladder question in exams assumes 1024.
- Confusing Mb (bits) with MB (bytes) in speed questions — divide by 8 to go bits → bytes.
Quick revision
- 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.
Types of questions asked
Every way this subtopic shows up in exams — how to recognise it, the formula or logic to use, and a solved example.
Type 1: Bit / nibble / byte definitionsvery common3 practice Q
'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.
Example: How many bits are there in 3 bytes?
3 × 8 = 24 bits — one byte always carries exactly 8 bits.
Type 2: KB → MB → GB → TB ladder conversionvery common6 practice Q
'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.
Example: A pen drive holds 4 GB. How many MB is that (exam convention)?
4 × 1024 = 4096 MB. Each step up the ladder multiplies by 1024, so going from GB to MB multiplies by 1024.
Type 3: Bits vs bytes in data-transfer speedcommon3 practice Q
'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.
Example: A connection delivers 16 Mbps (megabits per second). How many megabytes is that per second?
16 ÷ 8 = 2 MB per second — eight bits make one byte, so divide the bit-rate by 8.
Type 4: Unit odd-one-out and definitionscommon3 practice Q
'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).
Example: Which of the following is NOT a unit of data size?
Mbps — megabits per second, a speed unit. KB, MB and GB measure size.
Formulas
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)
Shortcut tricks
⚡ x1024 ladder
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.
Example: 2 GB = ? KB
2 x 1024 x 1024 = 2^21 = 2,048 KB x 1024 = 20,97,152 KB - or 2^21 KB.
⚡ Bit-vs-byte speed check
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.
Example: 16 Mbps line - max MB downloaded per second?
16/8 = 2 MB per second.
Where students lose marks
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).
Practice sets — 16 questions
Sets of 10, mixed across the question types above. Each answer comes with a step-by-step explanation.
Topic test · 10 questions
Suggested time 4 min · wrong answers go to your mistake notebook automatically.