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 255.255.255.252. How many usable host addresses H does it have?
255.255.255.252
H =
2.IPv4 subnettingHard
A router has routes to these networks: 10.98.178.0/24, 10.98.179.0/24, 10.98.180.0/24, 10.98.181.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.98.178.0/24 … 10.98.181.0/24
p =
3.Computer networksMedium
What is the main purpose of a VLAN?
- ATo split one physical switched network into separate broadcast domains
- BTo increase the speed of every switch port
- CTo give each device a public IP address
- DTo encrypt all traffic between switches so other departments cannot read it
4.Computer networksHard
Which of these addresses is a public (not RFC 1918 private) IPv4 address?
- A172.32.0.1
- B192.168.255.1
- C10.255.0.1
- D172.31.0.1
5.Number systemsMedium
Set the bits so they store −9 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −98 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 1001 0110 >> 3. What is the result's value R in decimal?
1001 0110>> 3
R =
3Solutions
1.IPv4 subnetting
Answer: H = 2
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
255.255.255.252 = /30
Usable hosts
22 − 2 = 2
Answer
H = 2
2.IPv4 subnetting
Answer: p = 21
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
178 = 10110010
181 = 10110101
common leading bits: 5
Prefix length
p = 16 + 5 = 21
Answer
p = /21
Summary route: 10.98.176.0/21 (it also covers 4 network(s) that are not in the list).
3.Computer networks
Answer: A · To split one physical switched network into separate broadcast domains
Why this is the answer
VLANs group ports logically, so broadcasts stay within each VLAN. This improves security and limits broadcast traffic.
Answer
A · To split one physical switched network into separate broadcast domains
4.Computer networks
Answer: A · 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
A · 172.32.0.1
5.Number systems
Answer: U = 247
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
9 = 0000 1001
inverted: 1111 0110
+1 → 1111 0111
Read it as unsigned
1111 0111₂ = 256 − 9 = 247
Answer
U = 247
6.Number systems
Answer: R = 18
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.
1001 0110 >> 3
= 0001 0010
Value of the result
0001 0010₂ = 18
Answer
R = 18
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