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 subnet uses the mask 255.255.254.0. How many usable host addresses H does it have?
255.255.254.0
H =
2.IPv4 subnettingHard
A router has routes to these networks: 10.116.205.0/24, 10.116.206.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.116.205.0/24 … 10.116.206.0/24
p =
3.Computer networksMedium
Why is UDP often preferred for live video calls?
- ALow delay matters more than retransmitting every lost packet
- BUDP guarantees every packet arrives, so the picture never freezes
- CUDP encrypts data automatically
- DUDP is required for all video
4.Computer networksHard
Why does a browser warn when a site presents a self-signed certificate?
- AThe site must be using HTTP instead of HTTPS
- BNo trusted certificate authority vouches that the key belongs to that site
- CSelf-signed certificates use no encryption at all, so the traffic is sent in clear text
- DThe certificate is always expired
5.Number systemsMedium
The 8-bit pattern 1001 1000 stores a signed integer in two's complement. What is its value N in decimal?
1001 10008 bit
N =
6.Number systemsHard
Set the bits to the 8-bit result of 1101 1111 XOR 1001 0101. What is the result's value R in decimal?
1101 1111XOR1001 0101
R =
3Solutions
1.IPv4 subnetting
Answer: H = 510
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).
Prefix length
255.255.254.0 = /23
Usable hosts
29 − 2 = 510
Answer
H = 510
2.IPv4 subnetting
Answer: p = 22
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
205 = 11001101
206 = 11001110
common leading bits: 6
Prefix length
p = 16 + 6 = 22
Answer
p = /22
Summary route: 10.116.204.0/22 (it also covers 2 network(s) that are not in the list).
3.Computer networks
Answer: A · Low delay matters more than retransmitting every lost packet
Why this is the answer
Retransmitting lost packets would add delay; real-time media tolerates some loss, so UDP-based protocols like RTP are used.
Answer
A · Low delay matters more than retransmitting every lost packet
4.Computer networks
Answer: B · No trusted certificate authority vouches that the key belongs to that site
Why this is the answer
Browsers trust certificates signed, directly or through a chain, by CAs in their trust store. A self-signed certificate could be made by anyone, such as a man-in-the-middle.
Answer
B · No trusted certificate authority vouches that the key belongs to that site
5.Number systems
Answer: N = −104
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.
Add the place values
The other bits keep their normal positive values.
−128 + 16 + 8 = −104
Answer
N = −104
6.Number systems
Answer: R = 74
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
XOR gives 1 where the two bits differ.
1101 1111
XOR 1001 0101
= 0100 1010
Value of the result
0100 1010₂ = 74
Answer
R = 74
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