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
A host has the address 10.20.155.170/29. What is the fourth octet x of its network address?
10.20.155.170/29
x =
3.Computer networksMedium
What is the main purpose of a VLAN?
- ATo encrypt all traffic between switches so other departments cannot read it
- BTo increase the speed of every switch port
- CTo give each device a public IP address
- DTo split one physical switched network into separate broadcast domains
4.Computer networksHard
Which routing protocol is a link-state protocol?
- AARP
- BBGP
- COSPF
- DRIP
5.Number systemsMedium
The 8-bit pattern 1100 0011 stores a signed integer in two's complement. What is its value N in decimal?
1100 00118 bit
N =
6.Number systemsHard
A system must give every one of 3085 items its own binary code of the same length. What is the smallest number of bits b needed?
3085
b = bit
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 = 168
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
23 = 8
Subnet of this host
network: ⌊170/8⌋·8 = 168
broadcast: 168 + 8 − 1 = 175
usable hosts: 169 … 174
Answer
x = 168
3.Computer networks
Answer: D · To split one physical switched network into separate broadcast domains
Why this is the answer
VLANs group ports logically, so broadcasts stay within each VLAN. This improves security and limits broadcast traffic.
Answer
D · To split one physical switched network into separate broadcast domains
4.Computer networks
Answer: C · OSPF
Why this is the answer
OSPF routers build a full map of the area and compute shortest paths with Dijkstra's algorithm. RIP is distance-vector; BGP is path-vector.
Answer
C · OSPF
5.Number systems
Answer: N = −61
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 + 64 + 2 + 1 = −61
Answer
N = −61
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 < 3085
212 = 4096 ≥ 3085
Answer
b = 12
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