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 192.168.93.0/24 is divided into /25 subnets, numbered 1, 2, 3, … from the lowest address (subnet 1 starts at .0). What is the fourth octet x of the network address of subnet 2?
192.168.93.0/24/25subnet 2 (subnet 1 starts at .0)
x =
2.IPv4 subnettingHard
A router has routes to these networks: 10.57.3.0/24, 10.57.4.0/24, 10.57.5.0/24, 10.57.6.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.57.3.0/24 … 10.57.6.0/24
p =
3.Computer networksMedium
Which of these is a private IPv4 address range?
- A192.168.0.0/16
- B100.0.0.0/8
- C200.1.1.0/24
- D8.8.8.0/24
4.Computer networksHard
In the TCP/IP model, which layer adds port numbers?
- ATransport layer
- BApplication layer
- CInternet layer
- DLink layer
5.Number systemsMedium
Write −69 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?
N = −698 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0110 0100 AND 0110 0100. What is the result's value R in decimal?
0110 0100AND0110 0100
R =
3Solutions
1.IPv4 subnetting
Answer: x = 128
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
27 = 128
Subnet number 2
network: (2 − 1)·128 = 128
broadcast: 128 + 128 − 1 = 255
Answer
x = 128
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
3 = 00000011
6 = 00000110
common leading bits: 5
Prefix length
p = 16 + 5 = 21
Answer
p = /21
Summary route: 10.57.0.0/21 (it also covers 4 network(s) that are not in the list).
3.Computer networks
Answer: A · 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
A · 192.168.0.0/16
4.Computer networks
Answer: A · Transport layer
Why this is the answer
TCP and UDP headers contain source and destination ports; the internet layer (IP) adds addresses.
Answer
A · Transport layer
5.Number systems
Answer: U = 187
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.
Invert and add one
69 = 0100 0101
inverted: 1011 1010
+1 → 1011 1011
Read it as unsigned
1011 1011₂ = 256 − 69 = 187
Answer
U = 187
6.Number systems
Answer: R = 100
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
AND gives 1 only where both bits are 1.
0110 0100
AND 0110 0100
= 0110 0100
Value of the result
0110 0100₂ = 100
Answer
R = 100
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