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 192.168.23.0/24 is split with VLSM for these LANs: A: 38 hosts, B: 15 hosts, C: 126 hosts, D: 9 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 B?
A: 38B: 15C: 126D: 9
x =
3.Computer networksMedium
What uniquely identifies one end of a TCP connection on the internet?
- AA MAC address alone
- BA domain name alone
- CAn IP address together with a port number
- DA subnet mask and gateway
4.Computer networksHard
An 8-port switch (no VLANs) has one host on each port. How many collision domains and broadcast domains are there?
- A8 collision domains, 8 broadcast domains
- B8 collision domains, 1 broadcast domain
- C1 collision domain, 1 broadcast domain
- D1 collision domain, 8 broadcast domains
5.Number systemsMedium
Set the bits so they store −83 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −838 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 1010 1000 XOR 0101 0111. What is the result's value R in decimal?
1010 1000XOR0101 0111
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 = 192
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
C: 126 hosts → 27 = 128 (/25)
A: 38 hosts → 26 = 64 (/26)
B: 15 hosts → 25 = 32 (/27)
D: 9 hosts → 24 = 16 (/28)
Allocation, largest first
C: .0 – .127
A: .128 – .191
B: .192 – .223
D: .224 – .239
Answer
x = 192
LAN B: 192.168.23.192/27.
3.Computer networks
Answer: C · An IP address together with a port number
Why this is the answer
A TCP connection is identified by source IP and port plus destination IP and port. Ports separate the many applications on one host.
Answer
C · An IP address together with a port number
4.Computer networks
Answer: B · 8 collision domains, 1 broadcast domain
Why this is the answer
Each switch port is its own collision domain, but broadcasts are forwarded to all ports, so the whole switch is one broadcast domain. A hub would give one of each.
Answer
B · 8 collision domains, 1 broadcast domain
5.Number systems
Answer: U = 173
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
83 = 0101 0011
inverted: 1010 1100
+1 → 1010 1101
Read it as unsigned
1010 1101₂ = 256 − 83 = 173
Answer
U = 173
6.Number systems
Answer: R = 255
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
XOR gives 1 where the two bits differ.
1010 1000
XOR 0101 0111
= 1111 1111
Value of the result
1111 1111₂ = 255
Answer
R = 255
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