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 department needs 1326 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
1326 hosts
p =
2.IPv4 subnettingHard
A router has routes to these networks: 10.206.122.0/24, 10.206.123.0/24, 10.206.124.0/24, 10.206.125.0/24, 10.206.126.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.206.122.0/24 … 10.206.126.0/24
p =
3.Computer networksMedium
What is a cyclic redundancy check (CRC) used for in Ethernet frames?
- ACorrecting every bit error automatically
- BChoosing the best route
- CEncrypting the frame
- DDetecting transmission errors
4.Computer networksHard
What does BGP mainly do on the internet?
- AExchanges routing information between autonomous systems
- BResolves names to addresses
- CAssigns IP addresses to home users through their internet providers
- DEncrypts data between routers
5.Number systemsMedium
Write −68 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?
N = −688 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0101 1100 >> 3. What is the result's value R in decimal?
0101 1100>> 3
R =
3Solutions
1.IPv4 subnetting
Answer: p = 21
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).
Host bits needed
210 − 2 = 1022 < 1326
211 − 2 = 2046 ≥ 1326 → h = 11
Prefix length
p = 32 − 11 = 21
Answer
p = /21
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
122 = 01111010
126 = 01111110
common leading bits: 5
Prefix length
p = 16 + 5 = 21
Answer
p = /21
Summary route: 10.206.120.0/21 (it also covers 3 network(s) that are not in the list).
3.Computer networks
Answer: D · Detecting transmission errors
Why this is the answer
The sender computes a CRC over the frame; the receiver recomputes it and discards the frame if they differ. CRC detects errors but does not correct them.
Answer
D · Detecting transmission errors
4.Computer networks
Answer: A · 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
A · Exchanges routing information between autonomous systems
5.Number systems
Answer: U = 188
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.
Invert and add one
68 = 0100 0100
inverted: 1011 1011
+1 → 1011 1100
Read it as unsigned
1011 1100₂ = 256 − 68 = 188
Answer
U = 188
6.Number systems
Answer: R = 11
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 right by 3 moves every bit 3 places to the right; bits that fall off the right end are lost and zeros come in on the left.
0101 1100 >> 3
= 0000 1011
Value of the result
0000 1011₂ = 11
Answer
R = 11
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