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 172.25.0.0/16 is divided into equal subnets with prefix /20. How many subnets N are there?
172.25.0.0/16/20
N =
2.IPv4 subnettingHard
A router has routes to these networks: 10.183.196.0/24, 10.183.197.0/24, 10.183.198.0/24, 10.183.199.0/24, 10.183.200.0/24, 10.183.201.0/24, 10.183.202.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.183.196.0/24 … 10.183.202.0/24
p =
3.Computer networksMedium
What is the IPv6 loopback address?
- A::1
- Bfe80::1
- C::
- Dff02::1
4.Computer networksHard
By the Nyquist formula, what is the maximum bit rate of a noiseless 3 kHz channel using 4 signal levels?
- A12 kbit/s
- B3 kbit/s
- C6 kbit/s
- D24 kbit/s
5.Number systemsMedium
Set the bits so they store −41 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −418 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0110 1010 << 1. What is the result's value R in decimal?
0110 1010<< 1
R =
3Solutions
1.IPv4 subnetting
Answer: N = 16
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
20 − 16 = 4
Number of subnets
N = 24 = 16
Answer
N = 16
Each /20 subnet has 212 − 2 = 4094 usable hosts.
2.IPv4 subnetting
Answer: p = 20
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
196 = 11000100
202 = 11001010
common leading bits: 4
Prefix length
p = 16 + 4 = 20
Answer
p = /20
Summary route: 10.183.192.0/20 (it also covers 9 network(s) that are not in the list).
3.Computer networks
Answer: A · ::1
Why this is the answer
::1 is the loopback address. :: is the unspecified address, fe80::/10 is link-local and ff02::1 is the all-nodes multicast group.
Answer
A · ::1
4.Computer networks
Answer: A · 12 kbit/s
Why this is the answer
2 × 3000 × log₂ 4 = 2 × 3000 × 2 = 12,000 bit/s. More levels raise the rate, but noise limits how many can be told apart.
Answer
A · 12 kbit/s
5.Number systems
Answer: U = 215
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
41 = 0010 1001
inverted: 1101 0110
+1 → 1101 0111
Read it as unsigned
1101 0111₂ = 256 − 41 = 215
Answer
U = 215
6.Number systems
Answer: R = 212
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
Shifting left by 1 moves every bit 1 places to the left; bits that fall off the left end are lost and zeros come in on the right.
0110 1010 << 1
= 1101 0100
Value of the result
1101 0100₂ = 212
Answer
R = 212
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