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 192.168.157.0/24 is divided into /26 subnets, numbered 1, 2, 3, … from the lowest address (subnet 1 starts at .0). What is the fourth octet x of the broadcast address of subnet 2?
192.168.157.0/24/26subnet 2 (subnet 1 starts at .0)
x =
2.IPv4 subnettingHard
A router has routes to these networks: 10.159.96.0/24, 10.159.97.0/24, 10.159.98.0/24, 10.159.99.0/24, 10.159.100.0/24, 10.159.101.0/24, 10.159.102.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.159.96.0/24 … 10.159.102.0/24
p =
3.Computer networksMedium
NAT (network address translation) is mainly used to:
- AIncrease the speed of a network cable
- BTranslate domain names into IP addresses for devices on a local network
- CLet many devices with private addresses share one public IP address
- DEncrypt traffic between two sites
4.Computer networksHard
What is the maximum transmission unit (MTU) of standard Ethernet payload?
- A65,535 bytes
- B64 bytes
- C1500 bytes
- D9000 bytes in every network
5.Number systemsMedium
The 8-bit pattern 1101 0000 stores a signed integer in two's complement. What is its value N in decimal?
1101 00008 bit
N =
6.Number systemsHard
Set the bits to the 8-bit result of 1010 0001 >> 1. What is the result's value R in decimal?
1010 0001>> 1
R =
3Solutions
1.IPv4 subnetting
Answer: x = 127
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
26 = 64
Subnet number 2
network: (2 − 1)·64 = 64
broadcast: 64 + 64 − 1 = 127
Answer
x = 127
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
96 = 01100000
102 = 01100110
common leading bits: 5
Prefix length
p = 16 + 5 = 21
Answer
p = /21
Summary route: 10.159.96.0/21 (it also covers 1 network(s) that are not in the list).
3.Computer networks
Answer: C · Let many devices with private addresses share one public IP address
Why this is the answer
NAT rewrites addresses (and ports) so private networks can access the internet through a smaller number of public addresses.
Answer
C · Let many devices with private addresses share one public IP address
4.Computer networks
Answer: C · 1500 bytes
Why this is the answer
Standard Ethernet carries up to 1500 bytes of payload; larger IP packets must be fragmented or use path MTU discovery.
Answer
C · 1500 bytes
5.Number systems
Answer: N = −48
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 + 64 + 16 = −48
Answer
N = −48
6.Number systems
Answer: R = 80
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 1 moves every bit 1 places to the right; bits that fall off the right end are lost and zeros come in on the left.
1010 0001 >> 1
= 0101 0000
Value of the result
0101 0000₂ = 80
Answer
R = 80
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