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 1016 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
1016 hosts
p =
2.IPv4 subnettingHard
A host has the address 10.20.26.172/27. What is the fourth octet x of the last usable host address in its subnet?
10.20.26.172/27
x =
3.Computer networksMedium
What is the IPv6 loopback address?
- Afe80::1
- Bff02::1
- C::1
- D::
4.Computer networksHard
What does the Diffie-Hellman key exchange achieve on its own, and what is its weakness?
- AIt agrees a shared secret over a public channel, but alone it is open to a man-in-the-middle
- BIt signs certificates for websites, but only works with short keys
- CIt authenticates both users with passwords, but needs a central server
- DIt encrypts bulk data directly over a public channel, but it is far too slow for large files and video
5.Number systemsMedium
The 8-bit pattern 1110 0110 stores a signed integer in two's complement. What is its value N in decimal?
1110 01108 bit
N =
6.Number systemsHard
Set the bits to the 8-bit result of 0111 0011 >> 2. What is the result's value R in decimal?
0111 0011>> 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 < 1016
210 − 2 = 1022 ≥ 1016 → h = 10
Prefix length
p = 32 − 10 = 22
Answer
p = /22
2.IPv4 subnetting
Answer: x = 190
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
25 = 32
Subnet of this host
network: ⌊172/32⌋·32 = 160
broadcast: 160 + 32 − 1 = 191
usable hosts: 161 … 190
Answer
x = 190
3.Computer networks
Answer: C · ::1
Why this is the answer
::1 is the loopback address. :: is the unspecified address, fe80::/10 is link-local and ff02::1 is the all-nodes multicast group.
Answer
C · ::1
4.Computer networks
Answer: A · 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
A · It agrees a shared secret over a public channel, but alone it is open to a man-in-the-middle
5.Number systems
Answer: N = −26
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 + 2 = −26
Answer
N = −26
6.Number systems
Answer: R = 28
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 right by 2 moves every bit 2 places to the right; bits that fall off the right end are lost and zeros come in on the left.
0111 0011 >> 2
= 0001 1100
Value of the result
0001 1100₂ = 28
Answer
R = 28
ExamProblems · examproblems.com/courses/computer-networks