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 192.168.219.0/24 is divided into /28 subnets, numbered 1, 2, 3, … from the lowest address (subnet 1 starts at .0). What is the fourth octet x of the network address of subnet 12?
192.168.219.0/24/28subnet 12 (subnet 1 starts at .0)
x =
2.IPv4 subnettingHard
A router has routes to these networks: 10.44.33.0/24, 10.44.34.0/24, 10.44.35.0/24, 10.44.36.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.44.33.0/24 … 10.44.36.0/24
p =
3.Computer networksMedium
What is the network address of the host 192.168.10.77/26?
- A192.168.10.76
- B192.168.10.0
- C192.168.10.64
- D192.168.10.128
4.Computer networksHard
A TCP connection has a 64 KB window and a 100 ms round-trip time, and no window scaling. What is its approximate maximum throughput?
- AAbout 5 Mbit/s
- BAbout 50 Mbit/s
- CAbout 0.5 Mbit/s
- DAbout 640 Mbit/s
5.Number systemsMedium
Set the bits so they store −59 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −598 bit
U =
6.Number systemsHard
A system must give every one of 3097 items its own binary code of the same length. What is the smallest number of bits b needed?
3097
b = bit
3Solutions
1.IPv4 subnetting
Answer: x = 176
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
24 = 16
Subnet number 12
network: (12 − 1)·16 = 176
broadcast: 176 + 16 − 1 = 191
Answer
x = 176
2.IPv4 subnetting
Answer: p = 21
Route summarisation: a summary route a.b.c.0/p covers all networks whose first p bits match. Write the differing octet of the first and last network in binary; the number of common leading bits, plus the bits of the octets before it, is the longest summary prefix.
Compare the bits
33 = 00100001
36 = 00100100
common leading bits: 5
Prefix length
p = 16 + 5 = 21
Answer
p = /21
Summary route: 10.44.32.0/21 (it also covers 4 network(s) that are not in the list).
3.Computer networks
Answer: C · 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
C · 192.168.10.64
4.Computer networks
Answer: A · About 5 Mbit/s
Why this is the answer
Throughput ≤ window / RTT = 65,536 × 8 bits / 0.1 s ≈ 5.2 Mbit/s, however fast the link is.
Answer
A · About 5 Mbit/s
5.Number systems
Answer: U = 197
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
59 = 0011 1011
inverted: 1100 0100
+1 → 1100 0101
Read it as unsigned
1100 0101₂ = 256 − 59 = 197
Answer
U = 197
6.Number systems
Answer: b = 12 bit
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.
Powers of two
211 = 2048 < 3097
212 = 4096 ≥ 3097
Answer
b = 12
ExamProblems · examproblems.com/courses/computer-networks