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 1390 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
1390 hosts
p =
2.IPv4 subnettingHard
A host has the address 10.20.6.179/30. What is the fourth octet x of the last usable host address in its subnet?
10.20.6.179/30
x =
3.Computer networksMedium
What is the role of a default gateway on a host?
- AIt assigns MAC addresses
- BIt is the router used for traffic to other networks
- CIt is the DNS server
- DIt is the switch port the host is connected to
4.Computer networksHard
A server's private key is stolen a year from now. Which TLS property keeps today's recorded sessions safe?
- ASending the certificate twice
- BUsing a longer domain name
- CCompressing the data before encryption
- DForward secrecy from ephemeral Diffie-Hellman key exchange
5.Number systemsMedium
The 8-bit pattern 0000 0101 stores a signed integer in two's complement. What is its value N in decimal?
0000 01018 bit
N =
6.Number systemsHard
Set the bits to the 8-bit result of 1100 1010 << 3. What is the result's value R in decimal?
1100 1010<< 3
R =
3Solutions
1.IPv4 subnetting
Answer: p = 21
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
210 − 2 = 1022 < 1390
211 − 2 = 2046 ≥ 1390 → h = 11
Prefix length
p = 32 − 11 = 21
Answer
p = /21
2.IPv4 subnetting
Answer: x = 178
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
22 = 4
Subnet of this host
network: ⌊179/4⌋·4 = 176
broadcast: 176 + 4 − 1 = 179
usable hosts: 177 … 178
Answer
x = 178
3.Computer networks
Answer: B · It is the router used for traffic to other networks
Why this is the answer
The host sends packets for non-local destinations to the default gateway, usually its local router.
Answer
B · It is the router used for traffic to other networks
4.Computer networks
Answer: D · Forward secrecy from ephemeral Diffie-Hellman key exchange
Why this is the answer
With ephemeral (EC)DHE, each session key is derived from temporary values that are discarded. The long-term key only signs the exchange, so stealing it later does not decrypt old traffic.
Answer
D · Forward secrecy from ephemeral Diffie-Hellman key exchange
5.Number systems
Answer: N = 5
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.
4 + 1 = 5
Answer
N = 5
6.Number systems
Answer: R = 80
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 left by 3 moves every bit 3 places to the left; bits that fall off the left end are lost and zeros come in on the right.
1100 1010 << 3
= 0101 0000
Value of the result
0101 0000₂ = 80
Answer
R = 80
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