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 976 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
976 hosts
p =
2.IPv4 subnettingHard
A host has the address 172.20.205.136/17. What is the third octet x of its subnet's broadcast address?
172.20.205.136/17
x =
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 encrypts every packet it forwards
- DIt tracks connections and allows replies that belong to established sessions
4.Computer networksHard
An attacker on a LAN sends forged ARP replies claiming the gateway's IP address. What is the likely result?
- AThe switch shuts down all of its ports
- BAll DNS queries fail across the internet
- CThe gateway's IP address is permanently changed to the attacker's address on every router
- DVictims send traffic for the gateway to the attacker, enabling a man-in-the-middle attack
5.Number systemsMedium
Set the bits so they store −57 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −578 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0111 0110 << 2. What is the result's value R in decimal?
0111 0110<< 2
R =
3Solutions
1.IPv4 subnetting
Answer: p = 22
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
29 − 2 = 510 < 976
210 − 2 = 1022 ≥ 976 → h = 10
Prefix length
p = 32 − 10 = 22
Answer
p = /22
2.IPv4 subnetting
Answer: x = 255
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 in the third octet
27 = 128
Subnet of this host
network: 172.20.128.0
broadcast: 172.20.255.255
Answer
x = 255
3.Computer networks
Answer: D · 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
D · It tracks connections and allows replies that belong to established sessions
4.Computer networks
Answer: D · Victims send traffic for the gateway to the attacker, enabling a man-in-the-middle attack
Why this is the answer
ARP spoofing poisons hosts' ARP caches with the attacker's MAC for the gateway IP. The attacker can then read, change or drop traffic; dynamic ARP inspection helps prevent it.
Answer
D · Victims send traffic for the gateway to the attacker, enabling a man-in-the-middle attack
5.Number systems
Answer: U = 199
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
57 = 0011 1001
inverted: 1100 0110
+1 → 1100 0111
Read it as unsigned
1100 0111₂ = 256 − 57 = 199
Answer
U = 199
6.Number systems
Answer: R = 216
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 left by 2 moves every bit 2 places to the left; bits that fall off the left end are lost and zeros come in on the right.
0111 0110 << 2
= 1101 1000
Value of the result
1101 1000₂ = 216
Answer
R = 216
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