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
A department needs 850 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
850 hosts
p =
2.IPv4 subnettingHard
A host has the address 10.20.92.241/27. What is the fourth octet x of its network address?
10.20.92.241/27
x =
3.Computer networksMedium
A router has routes for 10.0.0.0/8 and 10.1.0.0/16. Which route does it use for a packet to 10.1.5.5?
- A10.1.0.0/16, because it is the longest matching prefix
- BBoth routes, splitting the traffic equally
- C10.0.0.0/8, because it covers more addresses than the /16
- D10.0.0.0/8, because it was added first
4.Computer networksHard
Why does a browser warn when a site presents a self-signed certificate?
- AThe certificate is always expired
- BNo trusted certificate authority vouches that the key belongs to that site
- CSelf-signed certificates use no encryption at all, so the traffic is sent in clear text
- DThe site must be using HTTP instead of HTTPS
5.Number systemsMedium
Set the bits so they store −39 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −398 bit
U =
6.Number systemsHard
What is the most negative integer N that can be stored in 16-bit two's complement?
16 bit
N =
3Solutions
1.IPv4 subnetting
Answer: p = 22
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).
Host bits needed
29 − 2 = 510 < 850
210 − 2 = 1022 ≥ 850 → h = 10
Prefix length
p = 32 − 10 = 22
Answer
p = /22
2.IPv4 subnetting
Answer: x = 224
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
25 = 32
Subnet of this host
network: ⌊241/32⌋·32 = 224
broadcast: 224 + 32 − 1 = 255
usable hosts: 225 … 254
Answer
x = 224
3.Computer networks
Answer: A · 10.1.0.0/16, because it is the longest matching prefix
Why this is the answer
IP forwarding uses longest prefix match: among all routes that match the destination, the one with the longest mask is chosen.
Answer
A · 10.1.0.0/16, because it is the longest matching prefix
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 = 217
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.
Invert and add one
39 = 0010 0111
inverted: 1101 1000
+1 → 1101 1001
Read it as unsigned
1101 1001₂ = 256 − 39 = 217
Answer
U = 217
6.Number systems
Answer: N = −32768
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.
Most negative value
−215 = −32768
Answer
N = −32768
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