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 10.93.156.0/22 is divided into equal subnets with prefix /25. How many subnets N are there?
10.93.156.0/22/25
N =
2.IPv4 subnettingHard
A host has the address 172.20.134.164/17. What is the third octet x of its network address?
172.20.134.164/17
x =
3.Computer networksMedium
Which subnet mask corresponds to /20?
- A255.255.240.0
- B255.255.248.0
- C255.255.224.0
- D255.255.255.240
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
The 8-bit pattern 1111 1001 stores a signed integer in two's complement. What is its value N in decimal?
1111 10018 bit
N =
6.Number systemsHard
Set the bits to the 8-bit result of 0111 0110 XOR 1000 1001. What is the result's value R in decimal?
0111 0110XOR1000 1001
R =
3Solutions
1.IPv4 subnetting
Answer: N = 8
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).
Borrowed bits
25 − 22 = 3
Number of subnets
N = 23 = 8
Answer
N = 8
Each /25 subnet has 27 − 2 = 126 usable hosts.
2.IPv4 subnetting
Answer: x = 128
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 = 128
3.Computer networks
Answer: A · 255.255.240.0
Why this is the answer
/20 means 8 + 8 + 4 one-bits. Four one-bits in the third octet are 11110000 = 240, so the mask is 255.255.240.0.
Answer
A · 255.255.240.0
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: N = −7
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 + 16 + 8 + 1 = −7
Answer
N = −7
6.Number systems
Answer: R = 255
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
XOR gives 1 where the two bits differ.
0111 0110
XOR 1000 1001
= 1111 1111
Value of the result
1111 1111₂ = 255
Answer
R = 255
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