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 10.122.212.0/22 is divided into equal subnets with prefix /29. How many subnets N are there?
10.122.212.0/22/29
N =
2.IPv4 subnettingHard
A router has routes to these networks: 10.171.123.0/24, 10.171.124.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.171.123.0/24 … 10.171.124.0/24
p =
3.Computer networksMedium
What is a cyclic redundancy check (CRC) used for in Ethernet frames?
- AChoosing the best route
- BCorrecting every bit error automatically
- CEncrypting the frame
- DDetecting transmission errors
4.Computer networksHard
How does a content delivery network (CDN) mainly improve web performance?
- AIt increases the bandwidth of the users' own home connections
- BIt removes the need for DNS lookups
- CIt replaces TCP with a faster transport protocol
- DIt serves cached content from servers close to the users
5.Number systemsMedium
Set the bits so they store −115 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −1158 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0101 1010 AND 1001 1011. What is the result's value R in decimal?
0101 1010AND1001 1011
R =
3Solutions
1.IPv4 subnetting
Answer: N = 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).
Borrowed bits
29 − 22 = 7
Number of subnets
N = 27 = 128
Answer
N = 128
Each /29 subnet has 23 − 2 = 6 usable hosts.
2.IPv4 subnetting
Answer: p = 21
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
123 = 01111011
124 = 01111100
common leading bits: 5
Prefix length
p = 16 + 5 = 21
Answer
p = /21
Summary route: 10.171.120.0/21 (it also covers 6 network(s) that are not in the list).
3.Computer networks
Answer: D · 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
D · Detecting transmission errors
4.Computer networks
Answer: D · It serves cached content from servers close to the users
Why this is the answer
CDNs place copies of content at many edge locations and direct users, often via DNS, to a nearby server. This cuts latency and load on the origin.
Answer
D · It serves cached content from servers close to the users
5.Number systems
Answer: U = 141
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
115 = 0111 0011
inverted: 1000 1100
+1 → 1000 1101
Read it as unsigned
1000 1101₂ = 256 − 115 = 141
Answer
U = 141
6.Number systems
Answer: R = 26
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.
0101 1010
AND 1001 1011
= 0001 1010
Value of the result
0001 1010₂ = 26
Answer
R = 26
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