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 10.10.192.0/20 is divided into equal subnets with prefix /26. How many subnets N are there?
10.10.192.0/20/26
N =
2.IPv4 subnettingHard
A router has routes to these networks: 10.140.232.0/24, 10.140.233.0/24, 10.140.234.0/24, 10.140.235.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.140.232.0/24 … 10.140.235.0/24
p =
3.Computer networksMedium
Which of these is a private IPv4 address range?
- A192.168.0.0/16
- B100.0.0.0/8
- C8.8.8.0/24
- D200.1.1.0/24
4.Computer networksHard
By Shannon's theorem, what is the capacity of a 1 MHz channel with a signal-to-noise ratio of 255?
- A2 Mbit/s
- B8 Mbit/s
- C1 Mbit/s
- D255 Mbit/s
5.Number systemsMedium
The 8-bit pattern 1011 1100 stores a signed integer in two's complement. What is its value N in decimal?
1011 11008 bit
N =
6.Number systemsHard
An uncompressed image is 1280 × 720 pixels with 24 bits per pixel. How much memory M does it take, in KiB (1 KiB = 1024 bytes)?
1280 × 720 px24 bit/px1 KiB = 1024 B
M = KiB
3Solutions
1.IPv4 subnetting
Answer: N = 64
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
26 − 20 = 6
Number of subnets
N = 26 = 64
Answer
N = 64
Each /26 subnet has 26 − 2 = 62 usable hosts.
2.IPv4 subnetting
Answer: p = 22
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
232 = 11101000
235 = 11101011
common leading bits: 6
Prefix length
p = 16 + 6 = 22
Answer
p = /22
Summary route: 10.140.232.0/22
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: B · 8 Mbit/s
Why this is the answer
C = 10⁶ × log₂(256) = 10⁶ × 8 = 8 Mbit/s. This is the upper limit for error-free data rate on a noisy channel.
Answer
B · 8 Mbit/s
5.Number systems
Answer: N = −68
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 + 32 + 16 + 8 + 4 = −68
Answer
N = −68
6.Number systems
Answer: M = 2700 KiB
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.
Bits and bytes
1280·720·24 = 22118400 bit = 2764800 B
Convert to KiB
2764800/1024 = 2700 KiB
Answer
M = 2700 KiB
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