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 10.19.50.0/24 is divided into equal subnets with prefix /30. How many subnets N are there?
10.19.50.0/24/30
N =
2.IPv4 subnettingHard
A host has the address 10.20.105.248/29. What is the fourth octet x of the last usable host address in its subnet?
10.20.105.248/29
x =
3.Computer networksMedium
What is the main purpose of a VLAN?
- ATo split one physical switched network into separate broadcast domains
- BTo increase the speed of every switch port
- CTo give each device a public IP address
- DTo encrypt all traffic between switches so other departments cannot read it
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
- CChange the PC's subnet mask to /32
- DConfigure port forwarding on the router to the PC's private address
5.Number systemsMedium
Set the bits so they store −92 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −928 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0111 1001 AND 1110 0000. What is the result's value R in decimal?
0111 1001AND1110 0000
R =
3Solutions
1.IPv4 subnetting
Answer: N = 64
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
30 − 24 = 6
Number of subnets
N = 26 = 64
Answer
N = 64
Each /30 subnet has 22 − 2 = 2 usable hosts.
2.IPv4 subnetting
Answer: x = 254
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
23 = 8
Subnet of this host
network: ⌊248/8⌋·8 = 248
broadcast: 248 + 8 − 1 = 255
usable hosts: 249 … 254
Answer
x = 254
3.Computer networks
Answer: A · To split one physical switched network into separate broadcast domains
Why this is the answer
VLANs group ports logically, so broadcasts stay within each VLAN. This improves security and limits broadcast traffic.
Answer
A · To split one physical switched network into separate broadcast domains
4.Computer networks
Answer: D · 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
D · Configure port forwarding on the router to the PC's private address
5.Number systems
Answer: U = 164
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
92 = 0101 1100
inverted: 1010 0011
+1 → 1010 0100
Read it as unsigned
1010 0100₂ = 256 − 92 = 164
Answer
U = 164
6.Number systems
Answer: R = 96
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.
0111 1001
AND 1110 0000
= 0110 0000
Value of the result
0110 0000₂ = 96
Answer
R = 96
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