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
The network 10.226.208.0/20 is divided into equal subnets with prefix /24. How many subnets N are there?
10.226.208.0/20/24
N =
2.IPv4 subnettingHard
A host has the address 10.20.39.203/29. What is the last number (fourth octet) x of its subnet's broadcast address?
10.20.39.203/29
x =
3.Computer networksMedium
Which range of TCP/UDP port numbers is reserved as "well-known" ports?
- A0–65535
- B0–1023
- C1024–49151
- D49152–65535
4.Computer networksHard
Which mechanism prevents broadcast loops in a network with redundant switch links?
- ANAT
- BDHCP snooping
- CARP caching
- DSpanning Tree Protocol
5.Number systemsMedium
The 8-bit pattern 1000 1011 stores a signed integer in two's complement. What is its value N in decimal?
1000 10118 bit
N =
6.Number systemsHard
Set the bits to the 8-bit result of 1000 0001 >> 3. What is the result's value R in decimal?
1000 0001>> 3
R =
3Solutions
1.IPv4 subnetting
Answer: N = 16
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).
Borrowed bits
24 − 20 = 4
Number of subnets
N = 24 = 16
Answer
N = 16
Each /24 subnet has 28 − 2 = 254 usable hosts.
2.IPv4 subnetting
Answer: x = 207
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: ⌊203/8⌋·8 = 200
broadcast: 200 + 8 − 1 = 207
usable hosts: 201 … 206
Answer
x = 207
3.Computer networks
Answer: B · 0–1023
Why this is the answer
Ports 0–1023 are well-known ports for standard services. 1024–49151 are registered ports and 49152–65535 are dynamic or private ports.
Answer
B · 0–1023
4.Computer networks
Answer: D · 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
D · Spanning Tree Protocol
5.Number systems
Answer: N = −117
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.
Add the place values
The other bits keep their normal positive values.
−128 + 8 + 2 + 1 = −117
Answer
N = −117
6.Number systems
Answer: R = 16
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.
1000 0001 >> 3
= 0001 0000
Value of the result
0001 0000₂ = 16
Answer
R = 16
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