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 192.168.80.0/24 is divided into /27 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 4?
192.168.80.0/24/27subnet 4 (subnet 1 starts at .0)
x =
2.IPv4 subnettingHard
A router has routes to these networks: 10.129.114.0/24, 10.129.115.0/24, 10.129.116.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.129.114.0/24 … 10.129.116.0/24
p =
3.Computer networksMedium
What is the main purpose of a VLAN?
- ATo encrypt all traffic between switches so other departments cannot read it
- BTo split one physical switched network into separate broadcast domains
- CTo give each device a public IP address
- DTo increase the speed of every switch port
4.Computer networksHard
How does a content delivery network (CDN) mainly improve web performance?
- AIt replaces TCP with a faster transport protocol
- BIt removes the need for DNS lookups
- CIt increases the bandwidth of the users' own home connections
- DIt serves cached content from servers close to the users
5.Number systemsMedium
Set the bits so they store −107 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −1078 bit
U =
6.Number systemsHard
An uncompressed image is 1024 × 768 pixels with 16 bits per pixel. How much memory M does it take, in KiB (1 KiB = 1024 bytes)?
1024 × 768 px16 bit/px1 KiB = 1024 B
M = KiB
3Solutions
1.IPv4 subnetting
Answer: x = 96
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 number 4
network: (4 − 1)·32 = 96
broadcast: 96 + 32 − 1 = 127
Answer
x = 96
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
114 = 01110010
116 = 01110100
common leading bits: 5
Prefix length
p = 16 + 5 = 21
Answer
p = /21
Summary route: 10.129.112.0/21 (it also covers 5 network(s) that are not in the list).
3.Computer networks
Answer: B · To split one physical switched network into separate broadcast domains
Why this is the answer
VLANs group ports logically, so broadcasts stay within each VLAN. This improves security and limits broadcast traffic.
Answer
B · To split one physical switched network into separate broadcast domains
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 = 149
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
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: M = 1536 KiB
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.
Bits and bytes
1024·768·16 = 12582912 bit = 1572864 B
Convert to KiB
1572864/1024 = 1536 KiB
Answer
M = 1536 KiB
ExamProblems · examproblems.com/courses/computer-networks