Recall warm-up
- Which box joins different networks and picks where data goes next?
Stuck? Peek at 0.1.2 Nodes, links, topologies, LAN/WAN and the boxes in the middle
- Node = any device; host = node where messages start/end.
- Point-to-point (2 nodes) vs broadcast (all hear all).
- Simplex (one way) · half-duplex (two ways, one at a time) · full-duplex (both at once).
- Links: mesh n(n−1)/2, star n, ring n, tree n−1, bus 1 backbone.
- LAN (building) ⊂ WAN (cities) ⊂ the Internet (network of networks).
- Hub repeats to all · switch delivers within a LAN · router picks the next network.
- What physically travels on a link?
Stuck? Peek at 0.1.1 Why networks exist: hosts, links and sending data
- Network = devices + links that exchange data.
- Host = where a message starts or ends (laptop, phone, server).
- Link = physical path: copper (voltage), fibre (light), wireless (radio).
- All content → bits → signals → bits → content; meaning comes from an agreed encoding.
- One link per pair of n hosts: n(n − 1)/2 links — too many, so links are shared.
- How many private links do 5 hosts need for every pair?
Stuck? Peek at 0.1.1 Why networks exist: hosts, links and sending data
- Network = devices + links that exchange data.
- Host = where a message starts or ends (laptop, phone, server).
- Link = physical path: copper (voltage), fibre (light), wireless (radio).
- All content → bits → signals → bits → content; meaning comes from an agreed encoding.
- One link per pair of n hosts: n(n − 1)/2 links — too many, so links are shared.
The Hook
Your internet plan says "100 Mbps". Your download shows "12.5 MB/s". Which is faster? They are the same speed — and seeing why is the single most useful skill for GATE network numericals. Half of all wrong answers in delay questions come from mixing up bits with bytes or 1000 with 1024.
Predict First
A file is "1 KB". You send it at "1 kbps" (one kilobit per second). Guess: exactly 1 second, about 8 seconds, or about 8.2 seconds?
,About 8.2 seconds (8.192 s). Two traps at once: a byte is 8 bits, so the file is 8 × 1024 = 8192 bits; and "kilo" in kbps means 1000, so the rate is 1000 bits per second. 8192 / 1000 = 8.192 s. If a question says 1 KB = 1000 bytes, the answer becomes exactly 8 s.
Core Concept
Bit and byte
Notice the letter case: lower-case b = bit, upper-case B = byte. "100 Mb" is 100 megabits; "100 MB" is 100 megabytes, eight times more.
Rates use powers of 10
Speeds are counted in bits per second (bps), and their prefixes are decimal:
| Prefix | In a rate | Exact value |
|---|---|---|
| k (kilo) | kbps | 10³ = 1,000 bit/s |
| M (mega) | Mbps | 10⁶ = 1,000,000 bit/s |
| G (giga) | Gbps | 10⁹ bit/s |
Sizes use powers of 2
Memory and file sizes are built from powers of two, so their prefixes are binary:
| Prefix | In a size | Exact value |
|---|---|---|
| K | KB | 2¹⁰ = 1,024 bytes |
| M | MB | 2²⁰ = 1,048,576 bytes |
| G | GB | 2³⁰ = 1,073,741,824 bytes |
The conversion recipe
- Turn the size into bits: bytes × 8, with K = 1024, M = 2²⁰ (unless the question says otherwise).
- Turn the rate into bits per second: k = 10³, M = 10⁶, G = 10⁹.
- Time to push all bits out = bits ÷ (bits per second).
Time units
Network times are tiny, so we use:
| Unit | Seconds | Example |
|---|---|---|
| ms (millisecond) | 10⁻³ s | a message across a country |
| µs (microsecond) | 10⁻⁶ s | 1000 bits at 1 Gbps take 1 µs |
| ns (nanosecond) | 10⁻⁹ s | 1 bit at 1 Gbps takes 1 ns |
Putting it together
- Rates are decimal (k = 1000), sizes are binary (K = 1024), and 1 byte = 8 bits.
- Every timing question starts by converting the size to bits and the rate to bits per second.
- Follow the question's convention whenever it states one.
Visual
Worked Examples
How many bits are in a 5 KB file?
Show the full solution
5 KB = 5 × 1024 = 5120 bytes. Bits = 5120 × 8 = 40,960 bits.
A host sends a 1 KB file at 1 kbps. How long does it take to push all the bits out? Give the answer for both conventions.
Show the full solution
Default (KB = 1024 B): 1024 × 8 = 8192 bits; rate 1 kbps = 1000 bit/s. Time = 8192 / 1000 = 8.192 s.
If the question says 1 KB = 1000 B: 8000 / 1000 = 8 s.
A 2 MB file is sent over a 10 Mbps line. How long does pushing all bits out take (in seconds, to 3 decimals)? How large is the error if someone wrongly uses MB = 10⁶ bytes?
Show the full solution
Bits = 2 × 2²⁰ × 8 = 16,777,216. Rate = 10 × 10⁶ = 10⁷ bit/s. Time = 16,777,216 / 10⁷ = 1.678 s.
With MB = 10⁶: 2 × 10⁶ × 8 / 10⁷ = 1.6 s. The error is 0.078 s (about 4.9 %) — large enough to fall outside a GATE answer range.
GATE Traps
- kbps uses 10³, KB uses 2¹⁰. A 1 KB file at 1 kbps takes 8.192 s, not 8 s and not 1 s.
- Lower-case b = bit, upper-case B = byte. Mb vs MB differ by a factor of 8.
- "MB/s" in a download meter is a rate: it usually means 10⁶ bytes per second, not 2²⁰.
- When a question states "1 KB = 1000 bytes", follow it even though the default is 1024.
Memory Hook
"Speed is decimal, storage is binary." Rates count in thousands like money; sizes count in 1024s like memory chips.
Connect the Dots
We now count bits properly. This lesson's last step (bits ÷ rate) is the first delay formula of the course; it gets its proper name in Phase 1. Next (0.2.2): bits are written as binary numbers, and engineers write long binary numbers in a shorter base-16 form — how do we move between binary, decimal and that form quickly?
Self-Test
- NAT
How many bits are in 4 KB? (KB = 1024 bytes)
Write your answer before opening the key.
- NAT
A 1 MB file (MB = 2²⁰ bytes) is sent at 8 Mbps. Time to push all bits out, in seconds (3 decimals)?
Write your answer before opening the key.
- MCQ
1 Gbps equals:
- 2³⁰ bits per second
- 10⁹ bits per second
- 10⁹ bytes per second
- 2³⁰ bytes per second
- MSQ
Which statements are correct by default?
- 1 KB = 1024 bytes
- 1 kbps = 1024 bits per second
- 1 µs = 10⁻⁶ s
- 12.5 MB/s (rate) equals 100 Mbps
- NAT
How many nanoseconds does one bit take to leave a 100 Mbps line?
Write your answer before opening the key.
Rule Card
- 1 B = 8 b. Lower-case b = bit, upper-case B = byte.
- Rates: k = 10³, M = 10⁶, G = 10⁹ (bps).
- Sizes: K = 2¹⁰, M = 2²⁰, G = 2³⁰ (bytes) — unless the question says 1000.
- Time to push out = (size in bits) ÷ (rate in bit/s).
- ms = 10⁻³ s, µs = 10⁻⁶ s, ns = 10⁻⁹ s.
Concept Ledger
- bit (b)
- byte (B) = 8 bits
- bps, kbps, Mbps, Gbps (powers of 10)
- KB, MB, GB (powers of 2)
- ms, µs, ns
- time to push out = bits ÷ rate
Answer Vault
Try the questions first. Open when you are ready to check.
Warm-up answers
- A router.
- Bits, carried as signals (voltage, light, radio).
- 5 × 4 / 2 = 10.
Self-test answers
- 32768 — 4 × 1024 × 8 = 32,768 bits.
- 1.04..1.06 — 2²⁰ × 8 = 8,388,608 bits; ÷ 8 × 10⁶ = 1.048576 s ≈ 1.049 s.
- B — Rate prefixes are decimal and bps counts bits.
- A: Powers of 2 are for sizes, not rates.
- C: bps counts bits, not bytes.
- D: Wrong on both counts: rate prefixes are decimal and bps counts bits, not bytes.
- ACD — Sizes binary, rates decimal; µs = 10⁻⁶ s; 12.5 × 8 = 100.
- B: kbps is decimal: 1000 bits per second.
- 10 — 1 / 10⁸ s = 10⁻⁸ s = 10 ns.
Flashcards
- 1 kbps = ? and 1 KB = ?
Reveal answer
1 kbps = 1000 bit/s; 1 KB = 1024 bytes (default). - 100 Mbps in MB/s?
Reveal answer
12.5 (decimal megabytes per second). - Bits in 1 MB?
Reveal answer
2²⁰ × 8 = 8,388,608. - 1 bit at 1 Gbps takes?
Reveal answer
1 ns.
Exam shortcuts
- Bytes per second from bits per second: divide by 8. 100 Mbps = 12.5 MB/s (with MB = 10⁶ here, since it came from a rate). — converting a rate; both sides stay decimal because no file size is involved.
- 2¹⁰ ≈ 10³: quick estimate of 1024-based answers. — only for estimating which option is close; never for the final numerical-answer value (the 2.4 % error per K adds up).