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 1573 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
1573 hosts
p =
2.IPv4 subnettingHard
A router has routes to these networks: 10.99.164.0/24, 10.99.165.0/24, 10.99.166.0/24, 10.99.167.0/24, 10.99.168.0/24, 10.99.169.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.99.164.0/24 … 10.99.169.0/24
p =
3.Computer networksMedium
What is the role of a default gateway on a host?
- AIt is the DNS server
- BIt is the switch port the host is connected to
- CIt assigns MAC addresses
- DIt is the router used for traffic to other networks
4.Computer networksHard
After repeated collisions, classic Ethernet stations choose their waiting time from a range that doubles each time. Why?
- ATo synchronise all stations to one clock
- BTo lower the chance of colliding again when many stations compete
- CTo give the station with the highest MAC address priority on the shared cable
- DTo make the cable carry signals further
5.Number systemsMedium
The 8-bit pattern 1100 0000 stores a signed integer in two's complement. What is its value N in decimal?
1100 00008 bit
N =
6.Number systemsHard
Set the bits to the 8-bit result of 1101 0111 XOR 0011 1100. What is the result's value R in decimal?
1101 0111XOR0011 1100
R =
3Solutions
1.IPv4 subnetting
Answer: p = 21
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
210 − 2 = 1022 < 1573
211 − 2 = 2046 ≥ 1573 → h = 11
Prefix length
p = 32 − 11 = 21
Answer
p = /21
2.IPv4 subnetting
Answer: p = 20
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
164 = 10100100
169 = 10101001
common leading bits: 4
Prefix length
p = 16 + 4 = 20
Answer
p = /20
Summary route: 10.99.160.0/20 (it also covers 10 network(s) that are not in the list).
3.Computer networks
Answer: D · It is the router used for traffic to other networks
Why this is the answer
The host sends packets for non-local destinations to the default gateway, usually its local router.
Answer
D · It is the router used for traffic to other networks
4.Computer networks
Answer: B · 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
B · To lower the chance of colliding again when many stations compete
5.Number systems
Answer: N = −64
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 + 64 = −64
Answer
N = −64
6.Number systems
Answer: R = 235
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 0111
XOR 0011 1100
= 1110 1011
Value of the result
1110 1011₂ = 235
Answer
R = 235
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