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 subnet uses the mask 255.255.255.240. How many usable host addresses H does it have?
255.255.255.240
H =
2.IPv4 subnettingHard
A host has the address 10.20.10.20/30. What is the last number (fourth octet) x of its subnet's broadcast address?
10.20.10.20/30
x =
3.Computer networksMedium
HTTP is stateless. How do websites usually keep a user logged in across requests?
- ABy giving each user a fixed IP address
- BBy keeping the TCP connection open for days
- CWith cookies holding a session identifier or token
- DBy storing the password in the URL
4.Computer networksHard
You must divide 192.168.1.0/24 into at least 5 subnets with up to 25 hosts each. Which prefix length fits best?
- A/25
- B/27
- C/26
- D/28
5.Number systemsMedium
Set the bits so they store −117 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −1178 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: H = 14
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).
Prefix length
255.255.255.240 = /28
Usable hosts
24 − 2 = 14
Answer
H = 14
2.IPv4 subnetting
Answer: x = 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).
Block size
22 = 4
Subnet of this host
network: ⌊20/4⌋·4 = 20
broadcast: 20 + 4 − 1 = 23
usable hosts: 21 … 22
Answer
x = 23
3.Computer networks
Answer: C · With cookies holding a session identifier or token
Why this is the answer
The server sets a cookie containing a session ID or token, and the browser returns it with each request so the server can recognise the user.
Answer
C · With cookies holding a session identifier or token
4.Computer networks
Answer: B · /27
Why this is the answer
/27 gives 8 subnets with 30 usable hosts each. /26 gives only 4 subnets, and /28 allows only 14 hosts per subnet.
Answer
B · /27
5.Number systems
Answer: U = 139
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
117 = 0111 0101
inverted: 1000 1010
+1 → 1000 1011
Read it as unsigned
1000 1011₂ = 256 − 117 = 139
Answer
U = 139
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
ExamProblems · examproblems.com/courses/computer-networks