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 subnet uses the mask 255.255.255.248. How many usable host addresses H does it have?
255.255.255.248
H =
2.IPv4 subnettingHard
A router has routes to these networks: 10.222.119.0/24, 10.222.120.0/24, 10.222.121.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.222.119.0/24 … 10.222.121.0/24
p =
3.Computer networksMedium
Which single prefix summarises both 192.168.0.0/24 and 192.168.1.0/24?
- A192.168.1.0/23
- B192.168.0.0/23
- C192.168.0.0/22
- D192.168.0.0/25
4.Computer networksHard
In a SYN flood attack, what resource is the attacker trying to exhaust?
- AThe switch's MAC address table
- BThe server's disk space
- CThe server's table of half-open connections
- DThe DNS cache of the client
5.Number systemsMedium
Set the bits so they store −80 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −808 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0110 0100 AND 1011 1111. What is the result's value R in decimal?
0110 0100AND1011 1111
R =
3Solutions
1.IPv4 subnetting
Answer: H = 6
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).
Prefix length
255.255.255.248 = /29
Usable hosts
23 − 2 = 6
Answer
H = 6
2.IPv4 subnetting
Answer: p = 20
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
119 = 01110111
121 = 01111001
common leading bits: 4
Prefix length
p = 16 + 4 = 20
Answer
p = /20
Summary route: 10.222.112.0/20 (it also covers 13 network(s) that are not in the list).
3.Computer networks
Answer: B · 192.168.0.0/23
Why this is the answer
0 and 1 share all bits of the third octet except the last, so one bit less of prefix (/23) starting at 192.168.0.0 covers both exactly.
Answer
B · 192.168.0.0/23
4.Computer networks
Answer: C · The server's table of half-open connections
Why this is the answer
Each SYN makes the server reserve state and wait for an ACK that never comes. SYN cookies avoid storing state until the handshake completes.
Answer
C · The server's table of half-open connections
5.Number systems
Answer: U = 176
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
80 = 0101 0000
inverted: 1010 1111
+1 → 1011 0000
Read it as unsigned
1011 0000₂ = 256 − 80 = 176
Answer
U = 176
6.Number systems
Answer: R = 36
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
AND gives 1 only where both bits are 1.
0110 0100
AND 1011 1111
= 0010 0100
Value of the result
0010 0100₂ = 36
Answer
R = 36
ExamProblems · examproblems.com/courses/computer-networks