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 10.22.0.0/20 is divided into equal subnets with prefix /24. How many subnets N are there?
10.22.0.0/20/24
N =
2.IPv4 subnettingHard
The network 192.168.13.0/24 is split with VLSM for these LANs: A: 15 hosts, B: 121 hosts, C: 5 hosts, D: 24 hosts. Subnets are allocated from .0 upwards, the LAN with the most hosts first, each with the smallest subnet that fits. What is the fourth octet x of the network address of LAN C?
A: 15B: 121C: 5D: 24
x =
3.Computer networksMedium
Which protocol does the "ping" command use?
- AUDP
- BHTTP
- CTCP
- DICMP
4.Computer networksHard
Why does a browser warn when a site presents a self-signed certificate?
- ASelf-signed certificates use no encryption at all, so the traffic is sent in clear text
- BThe site must be using HTTP instead of HTTPS
- CNo trusted certificate authority vouches that the key belongs to that site
- DThe certificate is always expired
5.Number systemsMedium
Write −49 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?
N = −498 bit
U =
6.Number systemsHard
What is the largest unsigned integer N that fits in 12 bits?
12 bit
N =
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 = 192
VLSM: each LAN gets the smallest subnet with 2ʰ − 2 ≥ its host count, i.e. prefix 32 − h. Allocating the largest subnets first keeps every block aligned on a multiple of its own size, so the network addresses follow by adding up the block sizes.
Block size per LAN
B: 121 hosts → 27 = 128 (/25)
D: 24 hosts → 25 = 32 (/27)
A: 15 hosts → 25 = 32 (/27)
C: 5 hosts → 23 = 8 (/29)
Allocation, largest first
B: .0 – .127
D: .128 – .159
A: .160 – .191
C: .192 – .199
Answer
x = 192
LAN C: 192.168.13.192/29.
3.Computer networks
Answer: D · ICMP
Why this is the answer
Ping sends ICMP echo requests and measures the time until echo replies return.
Answer
D · ICMP
4.Computer networks
Answer: C · No trusted certificate authority vouches that the key belongs to that site
Why this is the answer
Browsers trust certificates signed, directly or through a chain, by CAs in their trust store. A self-signed certificate could be made by anyone, such as a man-in-the-middle.
Answer
C · No trusted certificate authority vouches that the key belongs to that site
5.Number systems
Answer: U = 207
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
49 = 0011 0001
inverted: 1100 1110
+1 → 1100 1111
Read it as unsigned
1100 1111₂ = 256 − 49 = 207
Answer
U = 207
6.Number systems
Answer: N = 4095
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.
Largest value
212 − 1 = 4095
Answer
N = 4095
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