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 192.168.248.0/24 is divided into /26 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 4?
192.168.248.0/24/26subnet 4 (subnet 1 starts at .0)
x =
2.IPv4 subnettingHard
A router has routes to these networks: 10.160.227.0/24, 10.160.228.0/24, 10.160.229.0/24, 10.160.230.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.160.227.0/24 … 10.160.230.0/24
p =
3.Computer networksMedium
Which medium access method did classic shared (half-duplex) Ethernet use?
- ACSMA/CA
- BTDMA
- CCSMA/CD
- DToken passing
4.Computer networksHard
What does the Diffie-Hellman key exchange achieve on its own, and what is its weakness?
- AIt signs certificates for websites, but only works with short keys
- BIt authenticates both users with passwords, but needs a central server
- CIt agrees a shared secret over a public channel, but alone it is open to a man-in-the-middle
- DIt encrypts bulk data directly over a public channel, but it is far too slow for large files and video
5.Number systemsMedium
Set the bits so they store −79 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −798 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 1010 1011 << 3. What is the result's value R in decimal?
1010 1011<< 3
R =
3Solutions
1.IPv4 subnetting
Answer: x = 192
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
26 = 64
Subnet number 4
network: (4 − 1)·64 = 192
broadcast: 192 + 64 − 1 = 255
Answer
x = 192
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
227 = 11100011
230 = 11100110
common leading bits: 5
Prefix length
p = 16 + 5 = 21
Answer
p = /21
Summary route: 10.160.224.0/21 (it also covers 4 network(s) that are not in the list).
3.Computer networks
Answer: C · CSMA/CD
Why this is the answer
Carrier sense multiple access with collision detection: stations stop when they detect a collision and retry after a random backoff. Full-duplex switched Ethernet has no collisions.
Answer
C · CSMA/CD
4.Computer networks
Answer: C · It agrees a shared secret over a public channel, but alone it is open to a man-in-the-middle
Why this is the answer
Diffie-Hellman lets two parties derive the same secret that eavesdroppers cannot compute. An attacker in the middle can run separate exchanges with each side unless the values are signed or otherwise authenticated.
Answer
C · It agrees a shared secret over a public channel, but alone it is open to a man-in-the-middle
5.Number systems
Answer: U = 177
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
79 = 0100 1111
inverted: 1011 0000
+1 → 1011 0001
Read it as unsigned
1011 0001₂ = 256 − 79 = 177
Answer
U = 177
6.Number systems
Answer: R = 88
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 3 moves every bit 3 places to the left; bits that fall off the left end are lost and zeros come in on the right.
1010 1011 << 3
= 0101 1000
Value of the result
0101 1000₂ = 88
Answer
R = 88
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