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 1015 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
1015 hosts
p =
2.IPv4 subnettingHard
The network 192.168.216.0/24 is split with VLSM for these LANs: A: 3 hosts, B: 23 hosts, C: 20 hosts, D: 65 hosts. Subnets are allocated from .0 upwards, the LAN with the most hosts first, each with the smallest subnet that fits. What is the fourth octet x of the network address of LAN B?
A: 3B: 23C: 20D: 65
x =
3.Computer networksMedium
What is the main purpose of a VLAN?
- ATo increase the speed of every switch port
- BTo give each device a public IP address
- CTo encrypt all traffic between switches so other departments cannot read it
- DTo split one physical switched network into separate broadcast domains
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 replaces TCP with a faster transport protocol
- CIt removes the need for DNS lookups
- DIt serves cached content from servers close to the users
5.Number systemsMedium
Set the bits so they store −78 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −788 bit
U =
6.Number systemsHard
A system must give every one of 4489 items its own binary code of the same length. What is the smallest number of bits b needed?
4489
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 < 1015
210 − 2 = 1022 ≥ 1015 → h = 10
Prefix length
p = 32 − 10 = 22
Answer
p = /22
2.IPv4 subnetting
Answer: x = 128
VLSM: each LAN gets the smallest subnet with 2ʰ − 2 ≥ its host count, i.e. prefix 32 − h. Allocating the largest subnets first keeps every block aligned on a multiple of its own size, so the network addresses follow by adding up the block sizes.
Block size per LAN
D: 65 hosts → 27 = 128 (/25)
B: 23 hosts → 25 = 32 (/27)
C: 20 hosts → 25 = 32 (/27)
A: 3 hosts → 23 = 8 (/29)
Allocation, largest first
D: .0 – .127
B: .128 – .159
C: .160 – .191
A: .192 – .199
Answer
x = 128
LAN B: 192.168.216.128/27.
3.Computer networks
Answer: D · 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
D · 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 = 178
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
78 = 0100 1110
inverted: 1011 0001
+1 → 1011 0010
Read it as unsigned
1011 0010₂ = 256 − 78 = 178
Answer
U = 178
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 < 4489
213 = 8192 ≥ 4489
Answer
b = 13
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