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 53 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
53 hosts
p =
2.IPv4 subnettingHard
A router has routes to these networks: 10.224.237.0/24, 10.224.238.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.224.237.0/24 … 10.224.238.0/24
p =
3.Computer networksMedium
Why does a switch sometimes send a frame out of all ports except the one it came in on?
- AThe destination MAC address is not yet in its address table
- BThe switch is acting as a router
- CThe frame is too large for one port
- DThe frame has a wrong IP checksum and must be checked by every host
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 encrypts bulk data directly over a public channel, but it is far too slow for large files and video
- CIt authenticates both users with passwords, but needs a central server
- DIt agrees a shared secret over a public channel, but alone it is open to a man-in-the-middle
5.Number systemsMedium
Write −107 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?
N = −1078 bit
U =
6.Number systemsHard
A system must give every one of 3449 items its own binary code of the same length. What is the smallest number of bits b needed?
3449
b = bit
3Solutions
1.IPv4 subnetting
Answer: p = 26
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
25 − 2 = 30 < 53
26 − 2 = 62 ≥ 53 → h = 6
Prefix length
p = 32 − 6 = 26
Answer
p = /26
2.IPv4 subnetting
Answer: p = 22
Route summarisation: a summary route a.b.c.0/p covers all networks whose first p bits match. Write the differing octet of the first and last network in binary; the number of common leading bits, plus the bits of the octets before it, is the longest summary prefix.
Compare the bits
237 = 11101101
238 = 11101110
common leading bits: 6
Prefix length
p = 16 + 6 = 22
Answer
p = /22
Summary route: 10.224.236.0/22 (it also covers 2 network(s) that are not in the list).
3.Computer networks
Answer: A · The destination MAC address is not yet in its address table
Why this is the answer
For an unknown unicast address the switch floods the frame. When the destination replies, the switch learns its port from the source MAC.
Answer
A · The destination MAC address is not yet in its address table
4.Computer networks
Answer: D · 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
D · 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 = 149
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
107 = 0110 1011
inverted: 1001 0100
+1 → 1001 0101
Read it as unsigned
1001 0101₂ = 256 − 107 = 149
Answer
U = 149
6.Number systems
Answer: b = 12 bit
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.
Powers of two
211 = 2048 < 3449
212 = 4096 ≥ 3449
Answer
b = 12
ExamProblems · examproblems.com/courses/computer-networks