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 192.168.50.0/24 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?
192.168.50.0/24/26subnet 3 (subnet 1 starts at .0)
x =
2.IPv4 subnettingHard
The network 192.168.120.0/24 is split with VLSM for these LANs: A: 88 hosts, B: 6 hosts, C: 17 hosts, D: 28 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: 88B: 6C: 17D: 28
x =
3.Computer networksMedium
Why does a switch sometimes send a frame out of all ports except the one it came in on?
- AThe switch is acting as a router
- BThe destination MAC address is not yet in its address table
- CThe frame is too large for one port
- DThe frame has a wrong IP checksum and must be checked by every host
4.Computer networksHard
What does BGP mainly do on the internet?
- AEncrypts data between routers
- BAssigns IP addresses to home users through their internet providers
- CResolves names to addresses
- DExchanges routing information between autonomous systems
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
Set the bits to the 8-bit result of 1011 1000 AND 0110 0101. What is the result's value R in decimal?
1011 1000AND0110 0101
R =
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 = 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
A: 88 hosts → 27 = 128 (/25)
D: 28 hosts → 25 = 32 (/27)
C: 17 hosts → 25 = 32 (/27)
B: 6 hosts → 23 = 8 (/29)
Allocation, largest first
A: .0 – .127
D: .128 – .159
C: .160 – .191
B: .192 – .199
Answer
x = 192
LAN B: 192.168.120.192/29.
3.Computer networks
Answer: B · The destination MAC address is not yet in its address table
Why this is the answer
For an unknown unicast address the switch floods the frame. When the destination replies, the switch learns its port from the source MAC.
Answer
B · The destination MAC address is not yet in its address table
4.Computer networks
Answer: D · 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
D · 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: R = 32
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.
1011 1000
AND 0110 0101
= 0010 0000
Value of the result
0010 0000₂ = 32
Answer
R = 32
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