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 67 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
67 hosts
p =
2.IPv4 subnettingHard
A host has the address 10.20.207.240/30. What is the fourth octet x of its network address?
10.20.207.240/30
x =
3.Computer networksMedium
What is the network address of the host 192.168.10.77/26?
- A192.168.10.64
- B192.168.10.128
- C192.168.10.76
- D192.168.10.0
4.Computer networksHard
Which of these addresses is a public (not RFC 1918 private) IPv4 address?
- A192.168.255.1
- B172.32.0.1
- C10.255.0.1
- D172.31.0.1
5.Number systemsMedium
Set the bits so they store −91 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −918 bit
U =
6.Number systemsHard
What is the most negative integer N that can be stored in 32-bit two's complement?
32 bit
N =
3Solutions
1.IPv4 subnetting
Answer: p = 25
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
26 − 2 = 62 < 67
27 − 2 = 126 ≥ 67 → h = 7
Prefix length
p = 32 − 7 = 25
Answer
p = /25
2.IPv4 subnetting
Answer: x = 240
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
22 = 4
Subnet of this host
network: ⌊240/4⌋·4 = 240
broadcast: 240 + 4 − 1 = 243
usable hosts: 241 … 242
Answer
x = 240
3.Computer networks
Answer: A · 192.168.10.64
Why this is the answer
/26 subnets start at 0, 64, 128 and 192. 77 lies in the block 64–127, so the network address is 192.168.10.64.
Answer
A · 192.168.10.64
4.Computer networks
Answer: B · 172.32.0.1
Why this is the answer
172.16.0.0/12 runs from 172.16.0.0 to 172.31.255.255, so 172.32.0.1 lies outside it. The other three are in private ranges.
Answer
B · 172.32.0.1
5.Number systems
Answer: U = 165
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
91 = 0101 1011
inverted: 1010 0100
+1 → 1010 0101
Read it as unsigned
1010 0101₂ = 256 − 91 = 165
Answer
U = 165
6.Number systems
Answer: N = −2.147 × 10⁹
Positional number systems: each digit is worth its value times a power of the base. In binary the places are worth 1, 2, 4, 8, 16, …; in hexadecimal 1, 16, 256, …, with A–F standing for 10–15. In 8-bit two's complement the leftmost bit is worth −128 instead of +128, which is how negative numbers are stored.
Most negative value
−231 = −2147483648
Answer
N = −2147483648
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