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 subnet uses the mask 255.255.252.0. How many usable host addresses H does it have?
255.255.252.0
H =
2.IPv4 subnettingHard
A host has the address 172.20.204.242/23. What is the third octet x of its network address?
172.20.204.242/23
x =
3.Computer networksMedium
Which subnet mask corresponds to /20?
- A255.255.224.0
- B255.255.240.0
- C255.255.255.240
- D255.255.248.0
4.Computer networksHard
An 8-port switch (no VLANs) has one host on each port. How many collision domains and broadcast domains are there?
- A1 collision domain, 8 broadcast domains
- B1 collision domain, 1 broadcast domain
- C8 collision domains, 1 broadcast domain
- D8 collision domains, 8 broadcast domains
5.Number systemsMedium
Set the bits so they store −56 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −568 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0010 0111 OR 0001 1010. What is the result's value R in decimal?
0010 0111OR0001 1010
R =
3Solutions
1.IPv4 subnetting
Answer: H = 1022
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).
Prefix length
255.255.252.0 = /22
Usable hosts
210 − 2 = 1022
Answer
H = 1022
2.IPv4 subnetting
Answer: x = 204
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 in the third octet
21 = 2
Subnet of this host
network: 172.20.204.0
broadcast: 172.20.205.255
Answer
x = 204
3.Computer networks
Answer: B · 255.255.240.0
Why this is the answer
/20 means 8 + 8 + 4 one-bits. Four one-bits in the third octet are 11110000 = 240, so the mask is 255.255.240.0.
Answer
B · 255.255.240.0
4.Computer networks
Answer: C · 8 collision domains, 1 broadcast domain
Why this is the answer
Each switch port is its own collision domain, but broadcasts are forwarded to all ports, so the whole switch is one broadcast domain. A hub would give one of each.
Answer
C · 8 collision domains, 1 broadcast domain
5.Number systems
Answer: U = 200
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
56 = 0011 1000
inverted: 1100 0111
+1 → 1100 1000
Read it as unsigned
1100 1000₂ = 256 − 56 = 200
Answer
U = 200
6.Number systems
Answer: R = 63
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.
0010 0111
OR 0001 1010
= 0011 1111
Value of the result
0011 1111₂ = 63
Answer
R = 63
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