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 824 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
824 hosts
p =
2.IPv4 subnettingHard
A router has routes to these networks: 10.201.20.0/24, 10.201.21.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.201.20.0/24 … 10.201.21.0/24
p =
3.Computer networksMedium
What is a cyclic redundancy check (CRC) used for in Ethernet frames?
- ADetecting transmission errors
- BChoosing the best route
- CCorrecting every bit error automatically
- DEncrypting the frame
4.Computer networksHard
An 8-port switch (no VLANs) has one host on each port. How many collision domains and broadcast domains are there?
- A1 collision domain, 8 broadcast domains
- B8 collision domains, 8 broadcast domains
- C8 collision domains, 1 broadcast domain
- D1 collision domain, 1 broadcast domain
5.Number systemsMedium
Write −44 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?
N = −448 bit
U =
6.Number systemsHard
A system must give every one of 2023 items its own binary code of the same length. What is the smallest number of bits b needed?
2023
b = bit
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 < 824
210 − 2 = 1022 ≥ 824 → h = 10
Prefix length
p = 32 − 10 = 22
Answer
p = /22
2.IPv4 subnetting
Answer: p = 23
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
20 = 00010100
21 = 00010101
common leading bits: 7
Prefix length
p = 16 + 7 = 23
Answer
p = /23
Summary route: 10.201.20.0/23
3.Computer networks
Answer: A · Detecting transmission errors
Why this is the answer
The sender computes a CRC over the frame; the receiver recomputes it and discards the frame if they differ. CRC detects errors but does not correct them.
Answer
A · Detecting transmission errors
4.Computer networks
Answer: C · 8 collision domains, 1 broadcast domain
Why this is the answer
Each switch port is its own collision domain, but broadcasts are forwarded to all ports, so the whole switch is one broadcast domain. A hub would give one of each.
Answer
C · 8 collision domains, 1 broadcast domain
5.Number systems
Answer: U = 212
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
44 = 0010 1100
inverted: 1101 0011
+1 → 1101 0100
Read it as unsigned
1101 0100₂ = 256 − 44 = 212
Answer
U = 212
6.Number systems
Answer: b = 11 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
210 = 1024 < 2023
211 = 2048 ≥ 2023
Answer
b = 11
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