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 172.24.0.0/16 is divided into equal subnets with prefix /20. How many subnets N are there?
172.24.0.0/16/20
N =
2.IPv4 subnettingHard
A host has the address 10.20.83.232/25. What is the fourth octet x of its network address?
10.20.83.232/25
x =
3.Computer networksMedium
Which of these is a private IPv4 address range?
- A100.0.0.0/8
- B8.8.8.0/24
- C200.1.1.0/24
- D192.168.0.0/16
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?
- AOptional RTS/CTS exchanges: the AP's CTS tells all nearby stations to wait
- BBy routing A's frames through C
- CBy making A and C use collision detection so they stop sending when frames overlap
- DBy increasing the TTL of the frames
5.Number systemsMedium
Set the bits so they store −53 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −538 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0011 0001 XOR 1000 0001. What is the result's value R in decimal?
0011 0001XOR1000 0001
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: x = 128
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: ⌊232/128⌋·128 = 128
broadcast: 128 + 128 − 1 = 255
usable hosts: 129 … 254
Answer
x = 128
3.Computer networks
Answer: D · 192.168.0.0/16
Why this is the answer
Private ranges are 10.0.0.0/8, 172.16.0.0/12 and 192.168.0.0/16; they are not routed on the public internet.
Answer
D · 192.168.0.0/16
4.Computer networks
Answer: A · 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
A · Optional RTS/CTS exchanges: the AP's CTS tells all nearby stations to wait
5.Number systems
Answer: U = 203
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
53 = 0011 0101
inverted: 1100 1010
+1 → 1100 1011
Read it as unsigned
1100 1011₂ = 256 − 53 = 203
Answer
U = 203
6.Number systems
Answer: R = 176
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.
0011 0001
XOR 1000 0001
= 1011 0000
Value of the result
1011 0000₂ = 176
Answer
R = 176
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