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
A department needs 1443 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
1443 hosts
p =
2.IPv4 subnettingHard
A router has routes to these networks: 10.232.208.0/24, 10.232.209.0/24, 10.232.210.0/24, 10.232.211.0/24, 10.232.212.0/24, 10.232.213.0/24, 10.232.214.0/24, 10.232.215.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.232.208.0/24 … 10.232.215.0/24
p =
3.Computer networksMedium
How does a stateful firewall differ from a simple packet filter?
- AIt only checks the MAC address of each frame
- BIt blocks all incoming traffic without exceptions, including replies to outgoing requests
- CIt tracks connections and allows replies that belong to established sessions
- DIt encrypts every packet it forwards
4.Computer networksHard
How does a content delivery network (CDN) mainly improve web performance?
- AIt replaces TCP with a faster transport protocol
- BIt increases the bandwidth of the users' own home connections
- CIt removes the need for DNS lookups
- DIt serves cached content from servers close to the users
5.Number systemsMedium
Set the bits so they store −82 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −828 bit
U =
6.Number systemsHard
What is the most negative integer N that can be stored in 16-bit two's complement?
16 bit
N =
3Solutions
1.IPv4 subnetting
Answer: p = 21
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).
Host bits needed
210 − 2 = 1022 < 1443
211 − 2 = 2046 ≥ 1443 → h = 11
Prefix length
p = 32 − 11 = 21
Answer
p = /21
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
208 = 11010000
215 = 11010111
common leading bits: 5
Prefix length
p = 16 + 5 = 21
Answer
p = /21
Summary route: 10.232.208.0/21
3.Computer networks
Answer: C · It tracks connections and allows replies that belong to established sessions
Why this is the answer
A stateful firewall keeps a table of active connections, so return traffic is allowed automatically. A stateless filter judges each packet in isolation.
Answer
C · It tracks connections and allows replies that belong to established sessions
4.Computer networks
Answer: D · It serves cached content from servers close to the users
Why this is the answer
CDNs place copies of content at many edge locations and direct users, often via DNS, to a nearby server. This cuts latency and load on the origin.
Answer
D · It serves cached content from servers close to the users
5.Number systems
Answer: U = 174
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
82 = 0101 0010
inverted: 1010 1101
+1 → 1010 1110
Read it as unsigned
1010 1110₂ = 256 − 82 = 174
Answer
U = 174
6.Number systems
Answer: N = −32768
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.
Most negative value
−215 = −32768
Answer
N = −32768
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