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 255.255.255.192. How many usable host addresses H does it have?
255.255.255.192
H =
2.IPv4 subnettingHard
A router has routes to these networks: 10.172.138.0/24, 10.172.139.0/24, 10.172.140.0/24, 10.172.141.0/24, 10.172.142.0/24, 10.172.143.0/24, 10.172.144.0/24, 10.172.145.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.172.138.0/24 … 10.172.145.0/24
p =
3.Computer networksMedium
What is the usual order of messages when a client obtains an address from DHCP?
- AOffer, Discover, Acknowledge, Request
- BDiscover, Offer, Request, Acknowledge
- CDiscover, Request, Offer, Acknowledge
- DRequest, Offer, Discover, Acknowledge
4.Computer networksHard
By the Nyquist formula, what is the maximum bit rate of a noiseless 3 kHz channel using 4 signal levels?
- A3 kbit/s
- B12 kbit/s
- C24 kbit/s
- D6 kbit/s
5.Number systemsMedium
The 8-bit pattern 0000 0011 stores a signed integer in two's complement. What is its value N in decimal?
0000 00118 bit
N =
6.Number systemsHard
What is the most negative integer N that can be stored in 12-bit two's complement?
12 bit
N =
3Solutions
1.IPv4 subnetting
Answer: H = 62
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
255.255.255.192 = /26
Usable hosts
26 − 2 = 62
Answer
H = 62
2.IPv4 subnetting
Answer: p = 19
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
138 = 10001010
145 = 10010001
common leading bits: 3
Prefix length
p = 16 + 3 = 19
Answer
p = /19
Summary route: 10.172.128.0/19 (it also covers 24 network(s) that are not in the list).
3.Computer networks
Answer: B · Discover, Offer, Request, Acknowledge
Why this is the answer
The client broadcasts Discover, servers reply with Offers, the client Requests one offer and the chosen server confirms with an Acknowledge.
Answer
B · Discover, Offer, Request, Acknowledge
4.Computer networks
Answer: B · 12 kbit/s
Why this is the answer
2 × 3000 × log₂ 4 = 2 × 3000 × 2 = 12,000 bit/s. More levels raise the rate, but noise limits how many can be told apart.
Answer
B · 12 kbit/s
5.Number systems
Answer: N = 3
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.
2 + 1 = 3
Answer
N = 3
6.Number systems
Answer: N = −2048
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.
Most negative value
−211 = −2048
Answer
N = −2048
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