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 255.255.255.128. How many usable host addresses H does it have?
255.255.255.128
H =
2.IPv4 subnettingHard
A router has routes to these networks: 10.200.96.0/24, 10.200.97.0/24, 10.200.98.0/24, 10.200.99.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.200.96.0/24 … 10.200.99.0/24
p =
3.Computer networksMedium
What does an MX record in DNS specify?
- AThe mail servers that accept email for a domain
- BThe IPv4 address of a web server
- CThe name servers for a zone
- DAn alias name for another host
4.Computer networksHard
After repeated collisions, classic Ethernet stations choose their waiting time from a range that doubles each time. Why?
- ATo make the cable carry signals further
- BTo give the station with the highest MAC address priority on the shared cable
- CTo lower the chance of colliding again when many stations compete
- DTo synchronise all stations to one clock
5.Number systemsMedium
Set the bits so they store −19 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −198 bit
U =
6.Number systemsHard
A system must give every one of 4647 items its own binary code of the same length. What is the smallest number of bits b needed?
4647
b = bit
3Solutions
1.IPv4 subnetting
Answer: H = 126
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
255.255.255.128 = /25
Usable hosts
27 − 2 = 126
Answer
H = 126
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
96 = 01100000
99 = 01100011
common leading bits: 6
Prefix length
p = 16 + 6 = 22
Answer
p = /22
Summary route: 10.200.96.0/22
3.Computer networks
Answer: A · The mail servers that accept email for a domain
Why this is the answer
MX (mail exchange) records list mail servers with priorities, so sending servers know where to deliver mail for that domain.
Answer
A · The mail servers that accept email for a domain
4.Computer networks
Answer: C · To lower the chance of colliding again when many stations compete
Why this is the answer
Each further collision suggests more contention, so the random range grows and stations are more likely to pick different slots. It adapts to load without central control.
Answer
C · To lower the chance of colliding again when many stations compete
5.Number systems
Answer: U = 237
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
19 = 0001 0011
inverted: 1110 1100
+1 → 1110 1101
Read it as unsigned
1110 1101₂ = 256 − 19 = 237
Answer
U = 237
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 < 4647
213 = 8192 ≥ 4647
Answer
b = 13
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