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 192.168.252.0/24 is divided into /25 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 2?
192.168.252.0/24/25subnet 2 (subnet 1 starts at .0)
x =
2.IPv4 subnettingHard
A router has routes to these networks: 10.171.24.0/24, 10.171.25.0/24, 10.171.26.0/24, 10.171.27.0/24, 10.171.28.0/24, 10.171.29.0/24, 10.171.30.0/24, 10.171.31.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.171.24.0/24 … 10.171.31.0/24
p =
3.Computer networksMedium
What is the role of a default gateway on a host?
- AIt is the switch port the host is connected to
- BIt assigns MAC addresses
- CIt is the router used for traffic to other networks
- DIt is the DNS server
4.Computer networksHard
What does BGP mainly do on the internet?
- AResolves names to addresses
- BAssigns IP addresses to home users through their internet providers
- CEncrypts data between routers
- DExchanges routing information between autonomous systems
5.Number systemsMedium
The 8-bit pattern 1001 1101 stores a signed integer in two's complement. What is its value N in decimal?
1001 11018 bit
N =
6.Number systemsHard
A system must give every one of 2489 items its own binary code of the same length. What is the smallest number of bits b needed?
2489
b = bit
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
27 = 128
Subnet number 2
network: (2 − 1)·128 = 128
broadcast: 128 + 128 − 1 = 255
Answer
x = 128
2.IPv4 subnetting
Answer: p = 21
Route summarisation: a summary route a.b.c.0/p covers all networks whose first p bits match. Write the differing octet of the first and last network in binary; the number of common leading bits, plus the bits of the octets before it, is the longest summary prefix.
Compare the bits
24 = 00011000
31 = 00011111
common leading bits: 5
Prefix length
p = 16 + 5 = 21
Answer
p = /21
Summary route: 10.171.24.0/21
3.Computer networks
Answer: C · It is the router used for traffic to other networks
Why this is the answer
The host sends packets for non-local destinations to the default gateway, usually its local router.
Answer
C · It is the router used for traffic to other networks
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: N = −99
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 + 16 + 8 + 4 + 1 = −99
Answer
N = −99
6.Number systems
Answer: b = 12 bit
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.
Powers of two
211 = 2048 < 2489
212 = 4096 ≥ 2489
Answer
b = 12
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