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
The network 192.168.31.0/24 is divided into /29 subnets, numbered 1, 2, 3, … from the lowest address (subnet 1 starts at .0). What is the fourth octet x of the broadcast address of subnet 4?
192.168.31.0/24/29subnet 4 (subnet 1 starts at .0)
x =
2.IPv4 subnettingHard
A host has the address 10.20.174.42/30. What is the fourth octet x of its network address?
10.20.174.42/30
x =
3.Computer networksMedium
Why does Wi-Fi use collision avoidance (CSMA/CA) instead of collision detection?
- AA wireless station cannot reliably detect collisions while it is transmitting
- BCollision detection only works on fibre cables, not on shared wireless radio channels
- CRadio signals never collide
- DWi-Fi only allows one device per network
4.Computer networksHard
What does BGP mainly do on the internet?
- AEncrypts data between routers
- BExchanges routing information between autonomous systems
- CAssigns IP addresses to home users through their internet providers
- DResolves names to addresses
5.Number systemsMedium
Write −49 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?
N = −498 bit
U =
6.Number systemsHard
A system must give every one of 4971 items its own binary code of the same length. What is the smallest number of bits b needed?
4971
b = bit
3Solutions
1.IPv4 subnetting
Answer: x = 31
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).
Block size
23 = 8
Subnet number 4
network: (4 − 1)·8 = 24
broadcast: 24 + 8 − 1 = 31
Answer
x = 31
2.IPv4 subnetting
Answer: x = 40
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).
Block size
22 = 4
Subnet of this host
network: ⌊42/4⌋·4 = 40
broadcast: 40 + 4 − 1 = 43
usable hosts: 41 … 42
Answer
x = 40
3.Computer networks
Answer: A · A wireless station cannot reliably detect collisions while it is transmitting
Why this is the answer
A radio transmitter cannot hear other weak signals while sending, and some stations are hidden from each other. So 802.11 waits random backoff times and uses acknowledgements.
Answer
A · A wireless station cannot reliably detect collisions while it is transmitting
4.Computer networks
Answer: B · Exchanges routing information between autonomous systems
Why this is the answer
BGP is the inter-domain routing protocol; autonomous systems advertise reachable prefixes and select paths based on policies.
Answer
B · Exchanges routing information between autonomous systems
5.Number systems
Answer: U = 207
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.
Invert and add one
49 = 0011 0001
inverted: 1100 1110
+1 → 1100 1111
Read it as unsigned
1100 1111₂ = 256 − 49 = 207
Answer
U = 207
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 < 4971
213 = 8192 ≥ 4971
Answer
b = 13
ExamProblems · examproblems.com/courses/computer-networks