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 255.255.248.0. How many usable host addresses H does it have?
255.255.248.0
H =
2.IPv4 subnettingHard
A router has routes to these networks: 10.91.32.0/24, 10.91.33.0/24, 10.91.34.0/24, 10.91.35.0/24, 10.91.36.0/24, 10.91.37.0/24, 10.91.38.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.91.32.0/24 … 10.91.38.0/24
p =
3.Computer networksMedium
Using even parity, which parity bit is added to the data bits 1011001?
- A4
- B2
- C0
- D1
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 0.5 Mbit/s
- BAbout 5 Mbit/s
- CAbout 640 Mbit/s
- DAbout 50 Mbit/s
5.Number systemsMedium
The 8-bit pattern 0100 0101 stores a signed integer in two's complement. What is its value N in decimal?
0100 01018 bit
N =
6.Number systemsHard
Set the bits to the 8-bit result of 0001 0100 XOR 1001 0101. What is the result's value R in decimal?
0001 0100XOR1001 0101
R =
3Solutions
1.IPv4 subnetting
Answer: H = 2046
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
255.255.248.0 = /21
Usable hosts
211 − 2 = 2046
Answer
H = 2046
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
32 = 00100000
38 = 00100110
common leading bits: 5
Prefix length
p = 16 + 5 = 21
Answer
p = /21
Summary route: 10.91.32.0/21 (it also covers 1 network(s) that are not in the list).
3.Computer networks
Answer: C · 0
Why this is the answer
1011001 contains four 1-bits, already an even number, so the parity bit is 0. With odd parity it would be 1.
Answer
C · 0
4.Computer networks
Answer: B · 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
B · About 5 Mbit/s
5.Number systems
Answer: N = 69
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.
Add the place values
The other bits keep their normal positive values.
64 + 4 + 1 = 69
Answer
N = 69
6.Number systems
Answer: R = 129
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
XOR gives 1 where the two bits differ.
0001 0100
XOR 1001 0101
= 1000 0001
Value of the result
1000 0001₂ = 129
Answer
R = 129
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