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 172.26.0.0/16 is divided into equal subnets with prefix /21. How many subnets N are there?
172.26.0.0/16/21
N =
2.IPv4 subnettingHard
A host has the address 10.20.58.57/30. What is the last number (fourth octet) x of its subnet's broadcast address?
10.20.58.57/30
x =
3.Computer networksMedium
A router has routes for 10.0.0.0/8 and 10.1.0.0/16. Which route does it use for a packet to 10.1.5.5?
- ABoth routes, splitting the traffic equally
- B10.0.0.0/8, because it covers more addresses than the /16
- C10.1.0.0/16, because it is the longest matching prefix
- D10.0.0.0/8, because it was added first
4.Computer networksHard
Which of these addresses is a public (not RFC 1918 private) IPv4 address?
- A172.31.0.1
- B172.32.0.1
- C10.255.0.1
- D192.168.255.1
5.Number systemsMedium
Write −3 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?
N = −38 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0001 1100 OR 0001 1000. What is the result's value R in decimal?
0001 1100OR0001 1000
R =
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
21 − 16 = 5
Number of subnets
N = 25 = 32
Answer
N = 32
Each /21 subnet has 211 − 2 = 2046 usable hosts.
2.IPv4 subnetting
Answer: x = 59
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: ⌊57/4⌋·4 = 56
broadcast: 56 + 4 − 1 = 59
usable hosts: 57 … 58
Answer
x = 59
3.Computer networks
Answer: C · 10.1.0.0/16, because it is the longest matching prefix
Why this is the answer
IP forwarding uses longest prefix match: among all routes that match the destination, the one with the longest mask is chosen.
Answer
C · 10.1.0.0/16, because it is the longest matching prefix
4.Computer networks
Answer: B · 172.32.0.1
Why this is the answer
172.16.0.0/12 runs from 172.16.0.0 to 172.31.255.255, so 172.32.0.1 lies outside it. The other three are in private ranges.
Answer
B · 172.32.0.1
5.Number systems
Answer: U = 253
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.
Invert and add one
3 = 0000 0011
inverted: 1111 1100
+1 → 1111 1101
Read it as unsigned
1111 1101₂ = 256 − 3 = 253
Answer
U = 253
6.Number systems
Answer: R = 28
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.
0001 1100
OR 0001 1000
= 0001 1100
Value of the result
0001 1100₂ = 28
Answer
R = 28
ExamProblems · examproblems.com/courses/computer-networks