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 716 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
716 hosts
p =
2.IPv4 subnettingHard
A router has routes to these networks: 10.112.87.0/24, 10.112.88.0/24, 10.112.89.0/24, 10.112.90.0/24, 10.112.91.0/24, 10.112.92.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.112.87.0/24 … 10.112.92.0/24
p =
3.Computer networksMedium
Which DNS record type maps a host name to an IPv6 address?
- AAAAA
- BMX
- CA
- DCNAME
4.Computer networksHard
How does a content delivery network (CDN) mainly improve web performance?
- AIt increases the bandwidth of the users' own home connections
- BIt replaces TCP with a faster transport protocol
- CIt serves cached content from servers close to the users
- DIt removes the need for DNS lookups
5.Number systemsMedium
Set the bits so they store −18 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −188 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0111 0101 >> 2. What is the result's value R in decimal?
0111 0101>> 2
R =
3Solutions
1.IPv4 subnetting
Answer: p = 22
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
29 − 2 = 510 < 716
210 − 2 = 1022 ≥ 716 → h = 10
Prefix length
p = 32 − 10 = 22
Answer
p = /22
2.IPv4 subnetting
Answer: p = 20
Route summarisation: a summary route a.b.c.0/p covers all networks whose first p bits match. Write the differing octet of the first and last network in binary; the number of common leading bits, plus the bits of the octets before it, is the longest summary prefix.
Compare the bits
87 = 01010111
92 = 01011100
common leading bits: 4
Prefix length
p = 16 + 4 = 20
Answer
p = /20
Summary route: 10.112.80.0/20 (it also covers 10 network(s) that are not in the list).
3.Computer networks
Answer: A · 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
A · AAAA
4.Computer networks
Answer: C · It serves cached content from servers close to the users
Why this is the answer
CDNs place copies of content at many edge locations and direct users, often via DNS, to a nearby server. This cuts latency and load on the origin.
Answer
C · It serves cached content from servers close to the users
5.Number systems
Answer: U = 238
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
18 = 0001 0010
inverted: 1110 1101
+1 → 1110 1110
Read it as unsigned
1110 1110₂ = 256 − 18 = 238
Answer
U = 238
6.Number systems
Answer: R = 29
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 2 moves every bit 2 places to the right; bits that fall off the right end are lost and zeros come in on the left.
0111 0101 >> 2
= 0001 1101
Value of the result
0001 1101₂ = 29
Answer
R = 29
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