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 192.168.152.0/24 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 3?
192.168.152.0/24/28subnet 3 (subnet 1 starts at .0)
x =
2.IPv4 subnettingHard
A router has routes to these networks: 10.153.32.0/24, 10.153.33.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.153.32.0/24 … 10.153.33.0/24
p =
3.Computer networksMedium
How many usable host addresses does a /26 IPv4 subnet have?
- A30
- B64
- C62
- D126
4.Computer networksHard
A DNS cache poisoning attack aims to:
- AOverload a server with traffic so that it stops answering queries
- BDelete DNS servers
- CSteal Wi-Fi passwords
- DMake a resolver store a false IP address for a domain
5.Number systemsMedium
Set the bits so they store −87 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −878 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0110 1110 >> 1. What is the result's value R in decimal?
0110 1110>> 1
R =
3Solutions
1.IPv4 subnetting
Answer: x = 47
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 3
network: (3 − 1)·16 = 32
broadcast: 32 + 16 − 1 = 47
Answer
x = 47
2.IPv4 subnetting
Answer: p = 23
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
32 = 00100000
33 = 00100001
common leading bits: 7
Prefix length
p = 16 + 7 = 23
Answer
p = /23
Summary route: 10.153.32.0/23
3.Computer networks
Answer: C · 62
Why this is the answer
A /26 has 6 host bits: 2⁶ = 64 addresses, minus the network and broadcast addresses, gives 62 usable hosts.
Answer
C · 62
4.Computer networks
Answer: D · Make a resolver store a false IP address for a domain
Why this is the answer
Poisoning inserts forged records into a resolver's cache. DNSSEC adds signatures so resolvers can verify records.
Answer
D · Make a resolver store a false IP address for a domain
5.Number systems
Answer: U = 169
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
87 = 0101 0111
inverted: 1010 1000
+1 → 1010 1001
Read it as unsigned
1010 1001₂ = 256 − 87 = 169
Answer
U = 169
6.Number systems
Answer: R = 55
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
Shifting right by 1 moves every bit 1 places to the right; bits that fall off the right end are lost and zeros come in on the left.
0110 1110 >> 1
= 0011 0111
Value of the result
0011 0111₂ = 55
Answer
R = 55
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