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 subnet uses the mask 255.255.248.0. How many usable host addresses H does it have?
255.255.248.0
H =
2.IPv4 subnettingHard
The network 192.168.129.0/24 is split with VLSM for these LANs: A: 84 hosts, B: 16 hosts, C: 21 hosts, D: 4 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 C?
A: 84B: 16C: 21D: 4
x =
3.Computer networksMedium
What does ARP do?
- AResolves domain names
- BAssigns IP addresses automatically to hosts when they join the local network
- CFinds the MAC address that belongs to an IP address on the local network
- DRoutes packets on the internet
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?
- AConfigure port forwarding on the router to the PC's private address
- BTurn off the PC's DNS client
- CGive the PC a different MAC address so the router can find it from outside
- DChange the PC's subnet mask to /32
5.Number systemsMedium
The 8-bit pattern 1000 1100 stores a signed integer in two's complement. What is its value N in decimal?
1000 11008 bit
N =
6.Number systemsHard
Set the bits to the 8-bit result of 1011 1010 OR 1111 0011. What is the result's value R in decimal?
1011 1010OR1111 0011
R =
3Solutions
1.IPv4 subnetting
Answer: H = 2046
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).
Prefix length
255.255.248.0 = /21
Usable hosts
211 − 2 = 2046
Answer
H = 2046
2.IPv4 subnetting
Answer: x = 128
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: 84 hosts → 27 = 128 (/25)
C: 21 hosts → 25 = 32 (/27)
B: 16 hosts → 25 = 32 (/27)
D: 4 hosts → 23 = 8 (/29)
Allocation, largest first
A: .0 – .127
C: .128 – .159
B: .160 – .191
D: .192 – .199
Answer
x = 128
LAN C: 192.168.129.128/27.
3.Computer networks
Answer: C · Finds the MAC address that belongs to an IP address on the local network
Why this is the answer
ARP broadcasts "who has this IP?" and the owner replies with its MAC address, so frames can be delivered locally.
Answer
C · Finds the MAC address that belongs to an IP address on the local network
4.Computer networks
Answer: A · 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
A · Configure port forwarding on the router to the PC's private address
5.Number systems
Answer: N = −116
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.
−128 + 8 + 4 = −116
Answer
N = −116
6.Number systems
Answer: R = 251
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
OR gives 1 where at least one bit is 1.
1011 1010
OR 1111 0011
= 1111 1011
Value of the result
1111 1011₂ = 251
Answer
R = 251
ExamProblems · examproblems.com/courses/computer-networks