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 255.255.248.0. How many usable host addresses H does it have?
255.255.248.0
H =
2.IPv4 subnettingHard
A host has the address 10.20.74.103/29. What is the fourth octet x of its network address?
10.20.74.103/29
x =
3.Computer networksMedium
Which subnet mask corresponds to /20?
- A255.255.224.0
- B255.255.240.0
- C255.255.248.0
- D255.255.255.240
4.Computer networksHard
What does BGP mainly do on the internet?
- AExchanges routing information between autonomous systems
- BAssigns IP addresses to home users through their internet providers
- CEncrypts data between routers
- DResolves names to addresses
5.Number systemsMedium
Set the bits so they store −106 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −1068 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 1011 0011 OR 1001 0110. What is the result's value R in decimal?
1011 0011OR1001 0110
R =
3Solutions
1.IPv4 subnetting
Answer: H = 2046
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
255.255.248.0 = /21
Usable hosts
211 − 2 = 2046
Answer
H = 2046
2.IPv4 subnetting
Answer: x = 96
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
23 = 8
Subnet of this host
network: ⌊103/8⌋·8 = 96
broadcast: 96 + 8 − 1 = 103
usable hosts: 97 … 102
Answer
x = 96
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: A · Exchanges routing information between autonomous systems
Why this is the answer
BGP is the inter-domain routing protocol; autonomous systems advertise reachable prefixes and select paths based on policies.
Answer
A · Exchanges routing information between autonomous systems
5.Number systems
Answer: U = 150
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
106 = 0110 1010
inverted: 1001 0101
+1 → 1001 0110
Read it as unsigned
1001 0110₂ = 256 − 106 = 150
Answer
U = 150
6.Number systems
Answer: R = 183
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.
1011 0011
OR 1001 0110
= 1011 0111
Value of the result
1011 0111₂ = 183
Answer
R = 183
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