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 1203 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
1203 hosts
p =
2.IPv4 subnettingHard
A host has the address 172.20.135.213/23. What is the third octet x of its network address?
172.20.135.213/23
x =
3.Computer networksMedium
How many usable host addresses does a /26 IPv4 subnet have?
- A62
- B30
- C64
- D126
4.Computer networksHard
What does BGP mainly do on the internet?
- AAssigns IP addresses to home users through their internet providers
- BExchanges routing information between autonomous systems
- CResolves names to addresses
- DEncrypts data between routers
5.Number systemsMedium
Set the bits so they store −31 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −318 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 1010 0001 >> 3. What is the result's value R in decimal?
1010 0001>> 3
R =
3Solutions
1.IPv4 subnetting
Answer: p = 21
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
210 − 2 = 1022 < 1203
211 − 2 = 2046 ≥ 1203 → h = 11
Prefix length
p = 32 − 11 = 21
Answer
p = /21
2.IPv4 subnetting
Answer: x = 134
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: 172.20.134.0
broadcast: 172.20.135.255
Answer
x = 134
3.Computer networks
Answer: A · 62
Why this is the answer
A /26 has 6 host bits: 2⁶ = 64 addresses, minus the network and broadcast addresses, gives 62 usable hosts.
Answer
A · 62
4.Computer networks
Answer: B · 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
B · Exchanges routing information between autonomous systems
5.Number systems
Answer: U = 225
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
31 = 0001 1111
inverted: 1110 0000
+1 → 1110 0001
Read it as unsigned
1110 0001₂ = 256 − 31 = 225
Answer
U = 225
6.Number systems
Answer: R = 20
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 right by 3 moves every bit 3 places to the right; bits that fall off the right end are lost and zeros come in on the left.
1010 0001 >> 3
= 0001 0100
Value of the result
0001 0100₂ = 20
Answer
R = 20
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