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 1057 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
1057 hosts
p =
2.IPv4 subnettingHard
A host has the address 10.20.255.250/29. What is the last number (fourth octet) x of its subnet's broadcast address?
10.20.255.250/29
x =
3.Computer networksMedium
Which of these is a private IPv4 address range?
- A100.0.0.0/8
- B192.168.0.0/16
- C200.1.1.0/24
- D8.8.8.0/24
4.Computer networksHard
Which mechanism prevents broadcast loops in a network with redundant switch links?
- AARP caching
- BSpanning Tree Protocol
- CNAT
- DDHCP snooping
5.Number systemsMedium
Set the bits so they store −97 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −978 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0001 1100 OR 0001 0110. What is the result's value R in decimal?
0001 1100OR0001 0110
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 < 1057
211 − 2 = 2046 ≥ 1057 → h = 11
Prefix length
p = 32 − 11 = 21
Answer
p = /21
2.IPv4 subnetting
Answer: x = 255
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
23 = 8
Subnet of this host
network: ⌊250/8⌋·8 = 248
broadcast: 248 + 8 − 1 = 255
usable hosts: 249 … 254
Answer
x = 255
3.Computer networks
Answer: B · 192.168.0.0/16
Why this is the answer
Private ranges are 10.0.0.0/8, 172.16.0.0/12 and 192.168.0.0/16; they are not routed on the public internet.
Answer
B · 192.168.0.0/16
4.Computer networks
Answer: B · Spanning Tree Protocol
Why this is the answer
STP elects a root bridge and blocks redundant paths, unblocking them if an active link fails.
Answer
B · Spanning Tree Protocol
5.Number systems
Answer: U = 159
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
97 = 0110 0001
inverted: 1001 1110
+1 → 1001 1111
Read it as unsigned
1001 1111₂ = 256 − 97 = 159
Answer
U = 159
6.Number systems
Answer: R = 30
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
OR gives 1 where at least one bit is 1.
0001 1100
OR 0001 0110
= 0001 1110
Value of the result
0001 1110₂ = 30
Answer
R = 30
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