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 192.168.242.0/24 is divided into /26 subnets, numbered 1, 2, 3, … from the lowest address (subnet 1 starts at .0). What is the fourth octet x of the network address of subnet 3?
192.168.242.0/24/26subnet 3 (subnet 1 starts at .0)
x =
2.IPv4 subnettingHard
The network 192.168.185.0/24 is split with VLSM for these LANs: A: 40 hosts, B: 45 hosts, C: 8 hosts, D: 16 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 A?
A: 40B: 45C: 8D: 16
x =
3.Computer networksMedium
Which subnet mask corresponds to /20?
- A255.255.248.0
- B255.255.224.0
- C255.255.240.0
- D255.255.255.240
4.Computer networksHard
What does BGP mainly do on the internet?
- AEncrypts data between routers
- BExchanges routing information between autonomous systems
- CAssigns IP addresses to home users through their internet providers
- DResolves names to addresses
5.Number systemsMedium
Set the bits so they store −44 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −448 bit
U =
6.Number systemsHard
An uncompressed image is 1920 × 1080 pixels with 32 bits per pixel. How much memory M does it take, in KiB (1 KiB = 1024 bytes)?
1920 × 1080 px32 bit/px1 KiB = 1024 B
M = KiB
3Solutions
1.IPv4 subnetting
Answer: x = 128
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
26 = 64
Subnet number 3
network: (3 − 1)·64 = 128
broadcast: 128 + 64 − 1 = 191
Answer
x = 128
2.IPv4 subnetting
Answer: x = 64
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
B: 45 hosts → 26 = 64 (/26)
A: 40 hosts → 26 = 64 (/26)
D: 16 hosts → 25 = 32 (/27)
C: 8 hosts → 24 = 16 (/28)
Allocation, largest first
B: .0 – .63
A: .64 – .127
D: .128 – .159
C: .160 – .175
Answer
x = 64
LAN A: 192.168.185.64/26.
3.Computer networks
Answer: C · 255.255.240.0
Why this is the answer
/20 means 8 + 8 + 4 one-bits. Four one-bits in the third octet are 11110000 = 240, so the mask is 255.255.240.0.
Answer
C · 255.255.240.0
4.Computer networks
Answer: B · Exchanges routing information between autonomous systems
Why this is the answer
BGP is the inter-domain routing protocol; autonomous systems advertise reachable prefixes and select paths based on policies.
Answer
B · Exchanges routing information between autonomous systems
5.Number systems
Answer: U = 212
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
44 = 0010 1100
inverted: 1101 0011
+1 → 1101 0100
Read it as unsigned
1101 0100₂ = 256 − 44 = 212
Answer
U = 212
6.Number systems
Answer: M = 8100 KiB
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.
Bits and bytes
1920·1080·32 = 66355200 bit = 8294400 B
Convert to KiB
8294400/1024 = 8100 KiB
Answer
M = 8100 KiB
ExamProblems · examproblems.com/courses/computer-networks