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 578 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
578 hosts
p =
2.IPv4 subnettingHard
A host has the address 10.20.166.240/30. What is the fourth octet x of its network address?
10.20.166.240/30
x =
3.Computer networksMedium
Which IPv4 header field stops packets from circulating forever in a routing loop?
- ATime to live (TTL)
- BType of service
- CHeader checksum
- DIdentification
4.Computer networksHard
What does BGP mainly do on the internet?
- AResolves names to addresses
- BExchanges routing information between autonomous systems
- CAssigns IP addresses to home users through their internet providers
- DEncrypts data between routers
5.Number systemsMedium
Set the bits so they store −45 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −458 bit
U =
6.Number systemsHard
A system must give every one of 2834 items its own binary code of the same length. What is the smallest number of bits b needed?
2834
b = bit
3Solutions
1.IPv4 subnetting
Answer: p = 22
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
29 − 2 = 510 < 578
210 − 2 = 1022 ≥ 578 → h = 10
Prefix length
p = 32 − 10 = 22
Answer
p = /22
2.IPv4 subnetting
Answer: x = 240
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: ⌊240/4⌋·4 = 240
broadcast: 240 + 4 − 1 = 243
usable hosts: 241 … 242
Answer
x = 240
3.Computer networks
Answer: A · Time to live (TTL)
Why this is the answer
Every router decrements the TTL; at zero the packet is discarded and an ICMP Time Exceeded message is usually sent. IPv6 calls it hop limit.
Answer
A · Time to live (TTL)
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 = 211
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
45 = 0010 1101
inverted: 1101 0010
+1 → 1101 0011
Read it as unsigned
1101 0011₂ = 256 − 45 = 211
Answer
U = 211
6.Number systems
Answer: b = 12 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
211 = 2048 < 2834
212 = 4096 ≥ 2834
Answer
b = 12
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