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 10.222.112.0/20 is divided into equal subnets with prefix /26. How many subnets N are there?
10.222.112.0/20/26
N =
2.IPv4 subnettingHard
A host has the address 10.20.210.175/28. What is the fourth octet x of the last usable host address in its subnet?
10.20.210.175/28
x =
3.Computer networksMedium
What is the main difference between the HTTP methods GET and POST?
- AGET retrieves a resource, POST submits data in the request body
- BGET is encrypted, POST is not
- CGET deletes a resource, POST reads it from the server's database
- DGET uses UDP, POST uses TCP
4.Computer networksHard
Stations A and C both reach access point B but cannot hear each other, so their frames collide at B. How does 802.11 help?
- ABy making A and C use collision detection so they stop sending when frames overlap
- BOptional RTS/CTS exchanges: the AP's CTS tells all nearby stations to wait
- CBy routing A's frames through C
- DBy increasing the TTL of the frames
5.Number systemsMedium
Set the bits so they store −20 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −208 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 1101 1000 << 2. What is the result's value R in decimal?
1101 1000<< 2
R =
3Solutions
1.IPv4 subnetting
Answer: N = 64
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 − 20 = 6
Number of subnets
N = 26 = 64
Answer
N = 64
Each /26 subnet has 26 − 2 = 62 usable hosts.
2.IPv4 subnetting
Answer: x = 174
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
24 = 16
Subnet of this host
network: ⌊175/16⌋·16 = 160
broadcast: 160 + 16 − 1 = 175
usable hosts: 161 … 174
Answer
x = 174
3.Computer networks
Answer: A · GET retrieves a resource, POST submits data in the request body
Why this is the answer
GET asks for a resource and should not change server state. POST sends data, such as a form, in the body for the server to process.
Answer
A · GET retrieves a resource, POST submits data in the request body
4.Computer networks
Answer: B · Optional RTS/CTS exchanges: the AP's CTS tells all nearby stations to wait
Why this is the answer
A station sends Request to Send; the AP answers Clear to Send, which every station in its range hears, so hidden stations defer for the reserved time.
Answer
B · Optional RTS/CTS exchanges: the AP's CTS tells all nearby stations to wait
5.Number systems
Answer: U = 236
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
20 = 0001 0100
inverted: 1110 1011
+1 → 1110 1100
Read it as unsigned
1110 1100₂ = 256 − 20 = 236
Answer
U = 236
6.Number systems
Answer: R = 96
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 2 moves every bit 2 places to the left; bits that fall off the left end are lost and zeros come in on the right.
1101 1000 << 2
= 0110 0000
Value of the result
0110 0000₂ = 96
Answer
R = 96
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