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 10.4.128.0/24 is divided into equal subnets with prefix /26. How many subnets N are there?
10.4.128.0/24/26
N =
2.IPv4 subnettingHard
A router has routes to these networks: 10.111.16.0/24, 10.111.17.0/24, 10.111.18.0/24, 10.111.19.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.111.16.0/24 … 10.111.19.0/24
p =
3.Computer networksMedium
Using even parity, which parity bit is added to the data bits 1011001?
- A0
- B2
- C4
- D1
4.Computer networksHard
What does TCP fast retransmit do?
- AResends a segment after three duplicate ACKs, without waiting for the timeout
- BResends every segment twice to be safe
- CDoubles the window after every loss
- DSkips the three-way handshake when reconnecting to known hosts, so data is resent sooner
5.Number systemsMedium
The 8-bit pattern 0010 1011 stores a signed integer in two's complement. What is its value N in decimal?
0010 10118 bit
N =
6.Number systemsHard
Set the bits to the 8-bit result of 0001 0110 XOR 0100 1000. What is the result's value R in decimal?
0001 0110XOR0100 1000
R =
3Solutions
1.IPv4 subnetting
Answer: N = 4
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
26 − 24 = 2
Number of subnets
N = 22 = 4
Answer
N = 4
Each /26 subnet has 26 − 2 = 62 usable hosts.
2.IPv4 subnetting
Answer: p = 22
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
16 = 00010000
19 = 00010011
common leading bits: 6
Prefix length
p = 16 + 6 = 22
Answer
p = /22
Summary route: 10.111.16.0/22
3.Computer networks
Answer: A · 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
A · 0
4.Computer networks
Answer: A · Resends a segment after three duplicate ACKs, without waiting for the timeout
Why this is the answer
Three duplicate ACKs strongly suggest a single lost segment, so TCP retransmits it at once. This recovers much faster than waiting for the retransmission timer.
Answer
A · Resends a segment after three duplicate ACKs, without waiting for the timeout
5.Number systems
Answer: N = 43
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.
32 + 8 + 2 + 1 = 43
Answer
N = 43
6.Number systems
Answer: R = 94
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 0110
XOR 0100 1000
= 0101 1110
Value of the result
0101 1110₂ = 94
Answer
R = 94
ExamProblems · examproblems.com/courses/computer-networks