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 10.44.250.0/24 is divided into equal subnets with prefix /28. How many subnets N are there?
10.44.250.0/24/28
N =
2.IPv4 subnettingHard
A host has the address 172.20.14.50/21. What is the third octet x of its subnet's broadcast address?
172.20.14.50/21
x =
3.Computer networksMedium
How does TLS typically use asymmetric and symmetric cryptography?
- AAsymmetric methods agree keys and authenticate; symmetric ciphers encrypt the data
- BOnly asymmetric cryptography is used throughout
- CSymmetric methods agree keys and authenticate; asymmetric ciphers encrypt all the data
- DOnly symmetric cryptography is used, with a fixed shared password
4.Computer networksHard
A student runs a game server on a PC behind a home NAT router. Friends on the internet cannot connect. What is the usual fix?
- ATurn off the PC's DNS client
- BGive the PC a different MAC address so the router can find it from outside
- CConfigure port forwarding on the router to the PC's private address
- DChange the PC's subnet mask to /32
5.Number systemsMedium
Set the bits so they store −94 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −948 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 1001 0110 AND 0011 0000. What is the result's value R in decimal?
1001 0110AND0011 0000
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
28 − 24 = 4
Number of subnets
N = 24 = 16
Answer
N = 16
Each /28 subnet has 24 − 2 = 14 usable hosts.
2.IPv4 subnetting
Answer: x = 15
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 in the third octet
23 = 8
Subnet of this host
network: 172.20.8.0
broadcast: 172.20.15.255
Answer
x = 15
3.Computer networks
Answer: A · Asymmetric methods agree keys and authenticate; symmetric ciphers encrypt the data
Why this is the answer
Public-key methods and certificates set up a shared secret and prove identity. Fast symmetric ciphers such as AES then protect the bulk data.
Answer
A · Asymmetric methods agree keys and authenticate; symmetric ciphers encrypt the data
4.Computer networks
Answer: C · Configure port forwarding on the router to the PC's private address
Why this is the answer
NAT creates mappings only for connections started from inside. A port-forwarding rule maps a public port to the internal host so inbound connections can reach it.
Answer
C · Configure port forwarding on the router to the PC's private address
5.Number systems
Answer: U = 162
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
94 = 0101 1110
inverted: 1010 0001
+1 → 1010 0010
Read it as unsigned
1010 0010₂ = 256 − 94 = 162
Answer
U = 162
6.Number systems
Answer: R = 16
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
AND gives 1 only where both bits are 1.
1001 0110
AND 0011 0000
= 0001 0000
Value of the result
0001 0000₂ = 16
Answer
R = 16
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