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 669 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
669 hosts
p =
2.IPv4 subnettingHard
A host has the address 10.20.78.76/26. What is the fourth octet x of its network address?
10.20.78.76/26
x =
3.Computer networksMedium
How many usable host addresses does a /24 IPv4 network have?
- A254
- B252
- C256
- D255
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
Write −93 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?
N = −938 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0010 1110 AND 0101 1110. What is the result's value R in decimal?
0010 1110AND0101 1110
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 < 669
210 − 2 = 1022 ≥ 669 → h = 10
Prefix length
p = 32 − 10 = 22
Answer
p = /22
2.IPv4 subnetting
Answer: x = 64
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
26 = 64
Subnet of this host
network: ⌊76/64⌋·64 = 64
broadcast: 64 + 64 − 1 = 127
usable hosts: 65 … 126
Answer
x = 64
3.Computer networks
Answer: A · 254
Why this is the answer
A /24 has 8 host bits, so 2⁸ = 256 addresses. The network and broadcast addresses are reserved, leaving 254 for hosts.
Answer
A · 254
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 = 163
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.
Invert and add one
93 = 0101 1101
inverted: 1010 0010
+1 → 1010 0011
Read it as unsigned
1010 0011₂ = 256 − 93 = 163
Answer
U = 163
6.Number systems
Answer: R = 14
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.
0010 1110
AND 0101 1110
= 0000 1110
Value of the result
0000 1110₂ = 14
Answer
R = 14
ExamProblems · examproblems.com/courses/computer-networks