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 713 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
713 hosts
p =
2.IPv4 subnettingHard
A host has the address 10.20.137.186/30. What is the fourth octet x of the last usable host address in its subnet?
10.20.137.186/30
x =
3.Computer networksMedium
What is the main difference between the HTTP methods GET and POST?
- AGET retrieves a resource, POST submits data in the request body
- BGET uses UDP, POST uses TCP
- CGET is encrypted, POST is not
- DGET deletes a resource, POST reads it from the server's database
4.Computer networksHard
What does the Diffie-Hellman key exchange achieve on its own, and what is its weakness?
- AIt signs certificates for websites, but only works with short keys
- BIt agrees a shared secret over a public channel, but alone it is open to a man-in-the-middle
- CIt encrypts bulk data directly over a public channel, but it is far too slow for large files and video
- DIt authenticates both users with passwords, but needs a central server
5.Number systemsMedium
Set the bits so they store −98 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −988 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 1101 1001 XOR 0011 0111. What is the result's value R in decimal?
1101 1001XOR0011 0111
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 < 713
210 − 2 = 1022 ≥ 713 → h = 10
Prefix length
p = 32 − 10 = 22
Answer
p = /22
2.IPv4 subnetting
Answer: x = 186
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
22 = 4
Subnet of this host
network: ⌊186/4⌋·4 = 184
broadcast: 184 + 4 − 1 = 187
usable hosts: 185 … 186
Answer
x = 186
3.Computer networks
Answer: A · GET retrieves a resource, POST submits data in the request body
Why this is the answer
GET asks for a resource and should not change server state. POST sends data, such as a form, in the body for the server to process.
Answer
A · GET retrieves a resource, POST submits data in the request body
4.Computer networks
Answer: B · It agrees a shared secret over a public channel, but alone it is open to a man-in-the-middle
Why this is the answer
Diffie-Hellman lets two parties derive the same secret that eavesdroppers cannot compute. An attacker in the middle can run separate exchanges with each side unless the values are signed or otherwise authenticated.
Answer
B · It agrees a shared secret over a public channel, but alone it is open to a man-in-the-middle
5.Number systems
Answer: U = 158
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
98 = 0110 0010
inverted: 1001 1101
+1 → 1001 1110
Read it as unsigned
1001 1110₂ = 256 − 98 = 158
Answer
U = 158
6.Number systems
Answer: R = 238
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.
1101 1001
XOR 0011 0111
= 1110 1110
Value of the result
1110 1110₂ = 238
Answer
R = 238
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