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 10.55.88.0/22 is divided into equal subnets with prefix /26. How many subnets N are there?
10.55.88.0/22/26
N =
2.IPv4 subnettingHard
The network 192.168.50.0/24 is split with VLSM for these LANs: A: 57 hosts, B: 42 hosts, C: 21 hosts, D: 9 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 B?
A: 57B: 42C: 21D: 9
x =
3.Computer networksMedium
What is the network address of the host 192.168.10.77/26?
- A192.168.10.76
- B192.168.10.128
- C192.168.10.64
- D192.168.10.0
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
- BNo trusted certificate authority vouches that the key belongs to that site
- CThe certificate is always expired
- DThe site must be using HTTP instead of HTTPS
5.Number systemsMedium
Write −102 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?
N = −1028 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0110 1100 >> 2. What is the result's value R in decimal?
0110 1100>> 2
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
26 − 22 = 4
Number of subnets
N = 24 = 16
Answer
N = 16
Each /26 subnet has 26 − 2 = 62 usable hosts.
2.IPv4 subnetting
Answer: x = 64
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
A: 57 hosts → 26 = 64 (/26)
B: 42 hosts → 26 = 64 (/26)
C: 21 hosts → 25 = 32 (/27)
D: 9 hosts → 24 = 16 (/28)
Allocation, largest first
A: .0 – .63
B: .64 – .127
C: .128 – .159
D: .160 – .175
Answer
x = 64
LAN B: 192.168.50.64/26.
3.Computer networks
Answer: C · 192.168.10.64
Why this is the answer
/26 subnets start at 0, 64, 128 and 192. 77 lies in the block 64–127, so the network address is 192.168.10.64.
Answer
C · 192.168.10.64
4.Computer networks
Answer: B · 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
B · No trusted certificate authority vouches that the key belongs to that site
5.Number systems
Answer: U = 154
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
102 = 0110 0110
inverted: 1001 1001
+1 → 1001 1010
Read it as unsigned
1001 1010₂ = 256 − 102 = 154
Answer
U = 154
6.Number systems
Answer: R = 27
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 2 moves every bit 2 places to the right; bits that fall off the right end are lost and zeros come in on the left.
0110 1100 >> 2
= 0001 1011
Value of the result
0001 1011₂ = 27
Answer
R = 27
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