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 1795 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
1795 hosts
p =
2.IPv4 subnettingHard
A host has the address 172.20.11.170/18. What is the third octet x of its subnet's broadcast address?
172.20.11.170/18
x =
3.Computer networksMedium
Which of these is a private IPv4 address range?
- A8.8.8.0/24
- B200.1.1.0/24
- C100.0.0.0/8
- D192.168.0.0/16
4.Computer networksHard
In a SYN flood attack, what resource is the attacker trying to exhaust?
- AThe server's table of half-open connections
- BThe server's disk space
- CThe switch's MAC address table
- DThe DNS cache of the client
5.Number systemsMedium
Set the bits so they store −12 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −128 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0110 1100 OR 0011 1011. What is the result's value R in decimal?
0110 1100OR0011 1011
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 < 1795
211 − 2 = 2046 ≥ 1795 → h = 11
Prefix length
p = 32 − 11 = 21
Answer
p = /21
2.IPv4 subnetting
Answer: x = 63
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 in the third octet
26 = 64
Subnet of this host
network: 172.20.0.0
broadcast: 172.20.63.255
Answer
x = 63
3.Computer networks
Answer: D · 192.168.0.0/16
Why this is the answer
Private ranges are 10.0.0.0/8, 172.16.0.0/12 and 192.168.0.0/16; they are not routed on the public internet.
Answer
D · 192.168.0.0/16
4.Computer networks
Answer: A · The server's table of half-open connections
Why this is the answer
Each SYN makes the server reserve state and wait for an ACK that never comes. SYN cookies avoid storing state until the handshake completes.
Answer
A · The server's table of half-open connections
5.Number systems
Answer: U = 244
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
12 = 0000 1100
inverted: 1111 0011
+1 → 1111 0100
Read it as unsigned
1111 0100₂ = 256 − 12 = 244
Answer
U = 244
6.Number systems
Answer: R = 127
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
OR gives 1 where at least one bit is 1.
0110 1100
OR 0011 1011
= 0111 1111
Value of the result
0111 1111₂ = 127
Answer
R = 127
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