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 192.168.240.0/24 is divided into /25 subnets, numbered 1, 2, 3, … from the lowest address (subnet 1 starts at .0). What is the fourth octet x of the network address of subnet 2?
192.168.240.0/24/25subnet 2 (subnet 1 starts at .0)
x =
2.IPv4 subnettingHard
A router has routes to these networks: 10.127.220.0/24, 10.127.221.0/24, 10.127.222.0/24, 10.127.223.0/24, 10.127.224.0/24, 10.127.225.0/24, 10.127.226.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.127.220.0/24 … 10.127.226.0/24
p =
3.Computer networksMedium
What characterises a distributed denial-of-service (DDoS) attack?
- AMany compromised machines flood a target with traffic
- BA virus deletes files on a single PC
- CAn attacker reads unencrypted Wi-Fi traffic from a nearby car
- DOne attacker guesses a user's password
4.Computer networksHard
By Shannon's theorem, what is the capacity of a 1 MHz channel with a signal-to-noise ratio of 255?
- A8 Mbit/s
- B255 Mbit/s
- C1 Mbit/s
- D2 Mbit/s
5.Number systemsMedium
Set the bits so they store −24 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −248 bit
U =
6.Number systemsHard
A system must give every one of 4909 items its own binary code of the same length. What is the smallest number of bits b needed?
4909
b = bit
3Solutions
1.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
27 = 128
Subnet number 2
network: (2 − 1)·128 = 128
broadcast: 128 + 128 − 1 = 255
Answer
x = 128
2.IPv4 subnetting
Answer: p = 18
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
220 = 11011100
226 = 11100010
common leading bits: 2
Prefix length
p = 16 + 2 = 18
Answer
p = /18
Summary route: 10.127.192.0/18 (it also covers 57 network(s) that are not in the list).
3.Computer networks
Answer: A · Many compromised machines flood a target with traffic
Why this is the answer
In a DDoS attack many sources overwhelm a server or link so legitimate users cannot be served. The many sources make simple blocking hard.
Answer
A · Many compromised machines flood a target with traffic
4.Computer networks
Answer: A · 8 Mbit/s
Why this is the answer
C = 10⁶ × log₂(256) = 10⁶ × 8 = 8 Mbit/s. This is the upper limit for error-free data rate on a noisy channel.
Answer
A · 8 Mbit/s
5.Number systems
Answer: U = 232
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
24 = 0001 1000
inverted: 1110 0111
+1 → 1110 1000
Read it as unsigned
1110 1000₂ = 256 − 24 = 232
Answer
U = 232
6.Number systems
Answer: b = 13 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
212 = 4096 < 4909
213 = 8192 ≥ 4909
Answer
b = 13
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