IPv4 subnetting
- Hosts per subnet
- 2(32 − prefix) − 2 (/31: 2, /32: 1)
- Block size
- 256 − (mask octet)
- Network address
- IP AND mask
- Broadcast address
- IP OR (NOT mask): all host bits set to 1
- Subnets from n borrowed bits
- 2n
Computer Networks: cram pack
Formula sheets, the key method steps for every topic and 6 practice problems, with full solutions at the back.
1Formulas and methods
Number systems
- Place values
- binary 2k, octal 8k, hex 16k
- To decimal
- Σ dk·bk
- From decimal
- divide by the base, read the remainders bottom-up
- Hex ↔ binary
- one hex digit = 4 bits
- Two’s complement
- invert the bits and add 1
2Practice problems
1.IPv4 subnettingMedium
The network 192.168.126.0/24 is divided into /28 subnets, numbered 1, 2, 3, … from the lowest address (subnet 1 starts at .0). What is the fourth octet x of the broadcast address of subnet 10?
192.168.126.0/24/28subnet 10 (subnet 1 starts at .0)
x =
2.IPv4 subnettingHard
A router has routes to these networks: 10.24.33.0/24, 10.24.34.0/24, 10.24.35.0/24, 10.24.36.0/24, 10.24.37.0/24, 10.24.38.0/24, 10.24.39.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.24.33.0/24 … 10.24.39.0/24
p =
3.Computer networksMedium
What does ARP do?
- AAssigns IP addresses automatically to hosts when they join the local network
- BRoutes packets on the internet
- CResolves domain names
- DFinds the MAC address that belongs to an IP address on the local network
4.Computer networksHard
After repeated collisions, classic Ethernet stations choose their waiting time from a range that doubles each time. Why?
- ATo give the station with the highest MAC address priority on the shared cable
- BTo synchronise all stations to one clock
- CTo lower the chance of colliding again when many stations compete
- DTo make the cable carry signals further
5.Number systemsMedium
Set the bits so they store −100 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −1008 bit
U =
6.Number systemsHard
An uncompressed image is 800 × 600 pixels with 8 bits per pixel. How much memory M does it take, in KiB (1 KiB = 1024 bytes)?
800 × 600 px8 bit/px1 KiB = 1024 B
M = KiB
3Solutions
1.IPv4 subnetting
Answer: x = 159
IPv4 subnetting: an address has 32 bits. The prefix /p says how many leading bits identify the network; the remaining 32 − p bits number the hosts. A subnet has 2³²⁻ᵖ addresses, but the first (network address) and last (broadcast address) cannot be given to hosts, so 2³²⁻ᵖ − 2 hosts fit. Exceptions: a /31 (point-to-point link, RFC 3021) uses both of its 2 addresses for hosts, and a /32 is one single address (a single host or a loopback).
Block size
24 = 16
Subnet number 10
network: (10 − 1)·16 = 144
broadcast: 144 + 16 − 1 = 159
Answer
x = 159
2.IPv4 subnetting
Answer: p = 21
Route summarisation: a summary route a.b.c.0/p covers all networks whose first p bits match. Write the differing octet of the first and last network in binary; the number of common leading bits, plus the bits of the octets before it, is the longest summary prefix.
Compare the bits
33 = 00100001
39 = 00100111
common leading bits: 5
Prefix length
p = 16 + 5 = 21
Answer
p = /21
Summary route: 10.24.32.0/21 (it also covers 1 network(s) that are not in the list).
3.Computer networks
Answer: D · Finds the MAC address that belongs to an IP address on the local network
Why this is the answer
ARP broadcasts "who has this IP?" and the owner replies with its MAC address, so frames can be delivered locally.
Answer
D · Finds the MAC address that belongs to an IP address on the local network
4.Computer networks
Answer: C · To lower the chance of colliding again when many stations compete
Why this is the answer
Each further collision suggests more contention, so the random range grows and stations are more likely to pick different slots. It adapts to load without central control.
Answer
C · To lower the chance of colliding again when many stations compete
5.Number systems
Answer: U = 156
Setting bits: each bit is worth a power of two (128, 64, …, 1). One hex digit is exactly four bits, and in 8-bit two's complement the leftmost bit is worth −128. Bitwise operations work on each bit position separately.
Invert and add one
100 = 0110 0100
inverted: 1001 1011
+1 → 1001 1100
Read it as unsigned
1001 1100₂ = 256 − 100 = 156
Answer
U = 156
6.Number systems
Answer: M = 468.8 KiB
Positional number systems: each digit is worth its value times a power of the base. In binary the places are worth 1, 2, 4, 8, 16, …; in hexadecimal 1, 16, 256, …, with A–F standing for 10–15. In 8-bit two's complement the leftmost bit is worth −128 instead of +128, which is how negative numbers are stored.
Bits and bytes
800·600·8 = 3840000 bit = 480000 B
Convert to KiB
480000/1024 = 468.75 KiB
Answer
M = 468.75 KiB
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