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 172.27.0.0/16 is divided into equal subnets with prefix /19. How many subnets N are there?
172.27.0.0/16/19
N =
2.IPv4 subnettingHard
A host has the address 172.20.38.163/21. What is the third octet x of its subnet's broadcast address?
172.20.38.163/21
x =
3.Computer networksMedium
A browser receives HTTP status code 404. What does it mean?
- AThe server had an internal error
- BThe requested resource was not found
- CThe request succeeded
- DThe client must log in first
4.Computer networksHard
In the TCP/IP model, which layer adds port numbers?
- ATransport layer
- BApplication layer
- CLink layer
- DInternet layer
5.Number systemsMedium
Set the bits so they store −22 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −228 bit
U =
6.Number systemsHard
A system must give every one of 2011 items its own binary code of the same length. What is the smallest number of bits b needed?
2011
b = bit
3Solutions
1.IPv4 subnetting
Answer: N = 8
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).
Borrowed bits
19 − 16 = 3
Number of subnets
N = 23 = 8
Answer
N = 8
Each /19 subnet has 213 − 2 = 8190 usable hosts.
2.IPv4 subnetting
Answer: x = 39
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 in the third octet
23 = 8
Subnet of this host
network: 172.20.32.0
broadcast: 172.20.39.255
Answer
x = 39
3.Computer networks
Answer: B · The requested resource was not found
Why this is the answer
404 Not Found means the server has no resource at that URL. 200 is OK, 401 is Unauthorized and 500 is Internal Server Error.
Answer
B · The requested resource was not found
4.Computer networks
Answer: A · Transport layer
Why this is the answer
TCP and UDP headers contain source and destination ports; the internet layer (IP) adds addresses.
Answer
A · Transport layer
5.Number systems
Answer: U = 234
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
22 = 0001 0110
inverted: 1110 1001
+1 → 1110 1010
Read it as unsigned
1110 1010₂ = 256 − 22 = 234
Answer
U = 234
6.Number systems
Answer: b = 11 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
210 = 1024 < 2011
211 = 2048 ≥ 2011
Answer
b = 11
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