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 8 equal subnets. If you borrow as few bits as possible, how many usable hosts H does each subnet have?
192.168.10.0/248 subnets
H =
2.IPv4 subnettingHard
The network 192.168.166.0/24 is split with VLSM for these LANs: A: 5 hosts, B: 39 hosts, C: 9 hosts, D: 13 hosts, E: 26 hosts. Subnets are allocated from .0 upwards, the LAN with the most hosts first, each with the smallest subnet that fits. What is the fourth octet x of the network address of LAN A?
A: 5B: 39C: 9D: 13E: 26
x =
3.Computer networksMedium
How does a stateful firewall differ from a simple packet filter?
- AIt encrypts every packet it forwards
- BIt only checks the MAC address of each frame
- CIt tracks connections and allows replies that belong to established sessions
- DIt blocks all incoming traffic without exceptions, including replies to outgoing requests
4.Computer networksHard
An attacker on a LAN sends forged ARP replies claiming the gateway's IP address. What is the likely result?
- AAll DNS queries fail across the internet
- BThe switch shuts down all of its ports
- CVictims send traffic for the gateway to the attacker, enabling a man-in-the-middle attack
- DThe gateway's IP address is permanently changed to the attacker's address on every router
5.Number systemsMedium
The 8-bit pattern 1110 0100 stores a signed integer in two's complement. What is its value N in decimal?
1110 01008 bit
N =
6.Number systemsHard
Set the bits to the 8-bit result of 0111 0101 << 2. What is the result's value R in decimal?
0111 0101<< 2
R =
3Solutions
1.IPv4 subnetting
Answer: H = 30
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
23 = 8 ≥ 8 → b = 3, /27
Hosts per subnet
25 − 2 = 30
Answer
H = 30
2.IPv4 subnetting
Answer: x = 128
VLSM: each LAN gets the smallest subnet with 2ʰ − 2 ≥ its host count, i.e. prefix 32 − h. Allocating the largest subnets first keeps every block aligned on a multiple of its own size, so the network addresses follow by adding up the block sizes.
Block size per LAN
B: 39 hosts → 26 = 64 (/26)
E: 26 hosts → 25 = 32 (/27)
D: 13 hosts → 24 = 16 (/28)
C: 9 hosts → 24 = 16 (/28)
A: 5 hosts → 23 = 8 (/29)
Allocation, largest first
B: .0 – .63
E: .64 – .95
D: .96 – .111
C: .112 – .127
A: .128 – .135
Answer
x = 128
LAN A: 192.168.166.128/29.
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: C · 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
C · Victims send traffic for the gateway to the attacker, enabling a man-in-the-middle attack
5.Number systems
Answer: N = −28
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 + 64 + 32 + 4 = −28
Answer
N = −28
6.Number systems
Answer: R = 212
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 0101 << 2
= 1101 0100
Value of the result
1101 0100₂ = 212
Answer
R = 212
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