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 1467 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
1467 hosts
p =
2.IPv4 subnettingHard
A host has the address 10.20.163.250/27. What is the fourth octet x of its network address?
10.20.163.250/27
x =
3.Computer networksMedium
Which DNS record type maps a host name to an IPv6 address?
- AMX
- BA
- CCNAME
- DAAAA
4.Computer networksHard
Why does TCP choose an unpredictable initial sequence number for each connection?
- ATo avoid confusion with old segments and make spoofed segments harder to inject
- BTo encrypt the payload of each segment
- CTo select the best route to the destination for the segments of that connection
- DTo compress the data more efficiently
5.Number systemsMedium
Set the bits so they store −90 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −908 bit
U =
6.Number systemsHard
A system must give every one of 573 items its own binary code of the same length. What is the smallest number of bits b needed?
573
b = bit
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 < 1467
211 − 2 = 2046 ≥ 1467 → h = 11
Prefix length
p = 32 − 11 = 21
Answer
p = /21
2.IPv4 subnetting
Answer: x = 224
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
25 = 32
Subnet of this host
network: ⌊250/32⌋·32 = 224
broadcast: 224 + 32 − 1 = 255
usable hosts: 225 … 254
Answer
x = 224
3.Computer networks
Answer: D · AAAA
Why this is the answer
An A record holds an IPv4 address, AAAA an IPv6 address. MX names mail servers and CNAME gives an alias.
Answer
D · AAAA
4.Computer networks
Answer: A · To avoid confusion with old segments and make spoofed segments harder to inject
Why this is the answer
Random initial sequence numbers stop delayed segments from old connections being accepted and make it hard for off-path attackers to forge valid segments.
Answer
A · To avoid confusion with old segments and make spoofed segments harder to inject
5.Number systems
Answer: U = 166
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
90 = 0101 1010
inverted: 1010 0101
+1 → 1010 0110
Read it as unsigned
1010 0110₂ = 256 − 90 = 166
Answer
U = 166
6.Number systems
Answer: b = 10 bit
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.
Powers of two
29 = 512 < 573
210 = 1024 ≥ 573
Answer
b = 10
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