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 10.220.160.0/20 is divided into equal subnets with prefix /25. How many subnets N are there?
10.220.160.0/20/25
N =
2.IPv4 subnettingHard
A host has the address 172.20.133.152/19. What is the third octet x of its subnet's broadcast address?
172.20.133.152/19
x =
3.Computer networksMedium
What is the network address of the host 192.168.10.77/26?
- A192.168.10.0
- B192.168.10.128
- C192.168.10.76
- D192.168.10.64
4.Computer networksHard
A DNS cache poisoning attack aims to:
- AOverload a server with traffic so that it stops answering queries
- BDelete DNS servers
- CMake a resolver store a false IP address for a domain
- DSteal Wi-Fi passwords
5.Number systemsMedium
Set the bits so they store −100 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −1008 bit
U =
6.Number systemsHard
What is the largest unsigned integer N that fits in 16 bits?
16 bit
N =
3Solutions
1.IPv4 subnetting
Answer: N = 32
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).
Borrowed bits
25 − 20 = 5
Number of subnets
N = 25 = 32
Answer
N = 32
Each /25 subnet has 27 − 2 = 126 usable hosts.
2.IPv4 subnetting
Answer: x = 159
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
25 = 32
Subnet of this host
network: 172.20.128.0
broadcast: 172.20.159.255
Answer
x = 159
3.Computer networks
Answer: D · 192.168.10.64
Why this is the answer
/26 subnets start at 0, 64, 128 and 192. 77 lies in the block 64–127, so the network address is 192.168.10.64.
Answer
D · 192.168.10.64
4.Computer networks
Answer: C · Make a resolver store a false IP address for a domain
Why this is the answer
Poisoning inserts forged records into a resolver's cache. DNSSEC adds signatures so resolvers can verify records.
Answer
C · Make a resolver store a false IP address for a domain
5.Number systems
Answer: U = 156
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
100 = 0110 0100
inverted: 1001 1011
+1 → 1001 1100
Read it as unsigned
1001 1100₂ = 256 − 100 = 156
Answer
U = 156
6.Number systems
Answer: N = 65535
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.
Largest value
216 − 1 = 65535
Answer
N = 65535
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