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 192.168.10.0/24 must be divided into at least 16 equal subnets. If you borrow as few bits as possible, how many usable hosts H does each subnet have?
192.168.10.0/2416 subnets
H =
2.IPv4 subnettingHard
A router has routes to these networks: 10.76.61.0/24, 10.76.62.0/24, 10.76.63.0/24, 10.76.64.0/24, 10.76.65.0/24, 10.76.66.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.76.61.0/24 … 10.76.66.0/24
p =
3.Computer networksMedium
TLS provides which security properties for HTTPS?
- AOnly faster loading
- BProtection against all malware and phishing on the visited site
- CAnonymity of the user
- DConfidentiality, integrity and server authentication
4.Computer networksHard
A student runs a game server on a PC behind a home NAT router. Friends on the internet cannot connect. What is the usual fix?
- AConfigure port forwarding on the router to the PC's private address
- BChange the PC's subnet mask to /32
- CGive the PC a different MAC address so the router can find it from outside
- DTurn off the PC's DNS client
5.Number systemsMedium
The 8-bit pattern 1011 0110 stores a signed integer in two's complement. What is its value N in decimal?
1011 01108 bit
N =
6.Number systemsHard
Set the bits to the 8-bit result of 1100 1111 OR 0110 1110. What is the result's value R in decimal?
1100 1111OR0110 1110
R =
3Solutions
1.IPv4 subnetting
Answer: H = 14
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).
Bits to borrow
24 = 16 ≥ 16 → b = 4, /28
Hosts per subnet
24 − 2 = 14
Answer
H = 14
2.IPv4 subnetting
Answer: p = 17
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
61 = 00111101
66 = 01000010
common leading bits: 1
Prefix length
p = 16 + 1 = 17
Answer
p = /17
Summary route: 10.76.0.0/17 (it also covers 122 network(s) that are not in the list).
3.Computer networks
Answer: D · Confidentiality, integrity and server authentication
Why this is the answer
TLS encrypts traffic, detects tampering and authenticates the server with certificates (optionally the client too).
Answer
D · Confidentiality, integrity and server authentication
4.Computer networks
Answer: A · Configure port forwarding on the router to the PC's private address
Why this is the answer
NAT creates mappings only for connections started from inside. A port-forwarding rule maps a public port to the internal host so inbound connections can reach it.
Answer
A · Configure port forwarding on the router to the PC's private address
5.Number systems
Answer: N = −74
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.
Add the place values
The other bits keep their normal positive values.
−128 + 32 + 16 + 4 + 2 = −74
Answer
N = −74
6.Number systems
Answer: R = 239
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.
Bit by bit
OR gives 1 where at least one bit is 1.
1100 1111
OR 0110 1110
= 1110 1111
Value of the result
1110 1111₂ = 239
Answer
R = 239
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