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 465 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
465 hosts
p =
2.IPv4 subnettingHard
A host has the address 10.20.143.179/27. What is the fourth octet x of the last usable host address in its subnet?
10.20.143.179/27
x =
3.Computer networksMedium
Which TCP flag signals that a sender has finished sending data?
- AURG
- BPSH
- CFIN
- DSYN
4.Computer networksHard
What does BGP mainly do on the internet?
- AAssigns IP addresses to home users through their internet providers
- BResolves names to addresses
- CExchanges routing information between autonomous systems
- DEncrypts data between routers
5.Number systemsMedium
Set the bits so they store −52 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −528 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0010 0110 AND 1000 1110. What is the result's value R in decimal?
0010 0110AND1000 1110
R =
3Solutions
1.IPv4 subnetting
Answer: p = 23
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
28 − 2 = 254 < 465
29 − 2 = 510 ≥ 465 → h = 9
Prefix length
p = 32 − 9 = 23
Answer
p = /23
2.IPv4 subnetting
Answer: x = 190
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
25 = 32
Subnet of this host
network: ⌊179/32⌋·32 = 160
broadcast: 160 + 32 − 1 = 191
usable hosts: 161 … 190
Answer
x = 190
3.Computer networks
Answer: C · FIN
Why this is the answer
Each side sends FIN when it has no more data, and the other side acknowledges it. SYN is for opening a connection; RST aborts one.
Answer
C · FIN
4.Computer networks
Answer: C · 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
C · Exchanges routing information between autonomous systems
5.Number systems
Answer: U = 204
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
52 = 0011 0100
inverted: 1100 1011
+1 → 1100 1100
Read it as unsigned
1100 1100₂ = 256 − 52 = 204
Answer
U = 204
6.Number systems
Answer: R = 6
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
AND gives 1 only where both bits are 1.
0010 0110
AND 1000 1110
= 0000 0110
Value of the result
0000 0110₂ = 6
Answer
R = 6
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