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 department needs 46 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
46 hosts
p =
2.IPv4 subnettingHard
A host has the address 10.20.247.178/25. What is the fourth octet x of the last usable host address in its subnet?
10.20.247.178/25
x =
3.Computer networksMedium
What is a cyclic redundancy check (CRC) used for in Ethernet frames?
- AChoosing the best route
- BCorrecting every bit error automatically
- CDetecting transmission errors
- DEncrypting the frame
4.Computer networksHard
What does the Diffie-Hellman key exchange achieve on its own, and what is its weakness?
- AIt agrees a shared secret over a public channel, but alone it is open to a man-in-the-middle
- BIt encrypts bulk data directly over a public channel, but it is far too slow for large files and video
- CIt signs certificates for websites, but only works with short keys
- DIt authenticates both users with passwords, but needs a central server
5.Number systemsMedium
The 8-bit pattern 0100 0000 stores a signed integer in two's complement. What is its value N in decimal?
0100 00008 bit
N =
6.Number systemsHard
Set the bits to the 8-bit result of 1101 1000 OR 0100 0100. What is the result's value R in decimal?
1101 1000OR0100 0100
R =
3Solutions
1.IPv4 subnetting
Answer: p = 26
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).
Host bits needed
25 − 2 = 30 < 46
26 − 2 = 62 ≥ 46 → h = 6
Prefix length
p = 32 − 6 = 26
Answer
p = /26
2.IPv4 subnetting
Answer: x = 254
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
27 = 128
Subnet of this host
network: ⌊178/128⌋·128 = 128
broadcast: 128 + 128 − 1 = 255
usable hosts: 129 … 254
Answer
x = 254
3.Computer networks
Answer: C · Detecting transmission errors
Why this is the answer
The sender computes a CRC over the frame; the receiver recomputes it and discards the frame if they differ. CRC detects errors but does not correct them.
Answer
C · Detecting transmission errors
4.Computer networks
Answer: A · 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
A · It agrees a shared secret over a public channel, but alone it is open to a man-in-the-middle
5.Number systems
Answer: N = 64
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 = 64
Answer
N = 64
6.Number systems
Answer: R = 220
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
OR gives 1 where at least one bit is 1.
1101 1000
OR 0100 0100
= 1101 1100
Value of the result
1101 1100₂ = 220
Answer
R = 220
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