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 10.5.224.0/20 is divided into equal subnets with prefix /26. How many subnets N are there?
10.5.224.0/20/26
N =
2.IPv4 subnettingHard
A router has routes to these networks: 10.214.135.0/24, 10.214.136.0/24, 10.214.137.0/24, 10.214.138.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.214.135.0/24 … 10.214.138.0/24
p =
3.Computer networksMedium
Which protocol does the "ping" command use?
- AICMP
- BTCP
- CHTTP
- DUDP
4.Computer networksHard
A remote-terminal application feels sluggish because small keystroke packets are held back. Which TCP mechanism is often responsible?
- ASlow start
- BThe three-way handshake
- CFast retransmit
- DNagle's algorithm
5.Number systemsMedium
The 8-bit pattern 1001 1001 stores a signed integer in two's complement. What is its value N in decimal?
1001 10018 bit
N =
6.Number systemsHard
Set the bits to the 8-bit result of 0010 1011 << 2. What is the result's value R in decimal?
0010 1011<< 2
R =
3Solutions
1.IPv4 subnetting
Answer: N = 64
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
26 − 20 = 6
Number of subnets
N = 26 = 64
Answer
N = 64
Each /26 subnet has 26 − 2 = 62 usable hosts.
2.IPv4 subnetting
Answer: p = 20
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
135 = 10000111
138 = 10001010
common leading bits: 4
Prefix length
p = 16 + 4 = 20
Answer
p = /20
Summary route: 10.214.128.0/20 (it also covers 12 network(s) that are not in the list).
3.Computer networks
Answer: A · ICMP
Why this is the answer
Ping sends ICMP echo requests and measures the time until echo replies return.
Answer
A · ICMP
4.Computer networks
Answer: D · Nagle's algorithm
Why this is the answer
Nagle's algorithm waits to bundle small segments while earlier data is unacknowledged. This saves bandwidth but adds delay for interactive traffic.
Answer
D · Nagle's algorithm
5.Number systems
Answer: N = −103
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 + 1 = −103
Answer
N = −103
6.Number systems
Answer: R = 172
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
Shifting left by 2 moves every bit 2 places to the left; bits that fall off the left end are lost and zeros come in on the right.
0010 1011 << 2
= 1010 1100
Value of the result
1010 1100₂ = 172
Answer
R = 172
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