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 192.168.53.0/24 is divided into /29 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 10?
192.168.53.0/24/29subnet 10 (subnet 1 starts at .0)
x =
2.IPv4 subnettingHard
A host has the address 10.20.166.218/30. What is the last number (fourth octet) x of its subnet's broadcast address?
10.20.166.218/30
x =
3.Computer networksMedium
Which protocol does the "ping" command use?
- AICMP
- BHTTP
- CUDP
- DTCP
4.Computer networksHard
DNS queries normally use UDP. When does DNS typically use TCP instead?
- AFor responses too large for UDP and for zone transfers
- BFor every query sent from a web browser
- COnly when the domain name is longer than ten characters
- DOnly for reverse lookups of IP addresses
5.Number systemsMedium
Set the bits so they store −106 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −1068 bit
U =
6.Number systemsHard
A system must give every one of 442 items its own binary code of the same length. What is the smallest number of bits b needed?
442
b = bit
3Solutions
1.IPv4 subnetting
Answer: x = 72
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 number 10
network: (10 − 1)·8 = 72
broadcast: 72 + 8 − 1 = 79
Answer
x = 72
2.IPv4 subnetting
Answer: x = 219
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
22 = 4
Subnet of this host
network: ⌊218/4⌋·4 = 216
broadcast: 216 + 4 − 1 = 219
usable hosts: 217 … 218
Answer
x = 219
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: A · For responses too large for UDP and for zone transfers
Why this is the answer
If a UDP response is truncated, the resolver retries over TCP. Zone transfers between name servers also use TCP because they carry lots of data.
Answer
A · For responses too large for UDP and for zone transfers
5.Number systems
Answer: U = 150
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
106 = 0110 1010
inverted: 1001 0101
+1 → 1001 0110
Read it as unsigned
1001 0110₂ = 256 − 106 = 150
Answer
U = 150
6.Number systems
Answer: b = 9 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
28 = 256 < 442
29 = 512 ≥ 442
Answer
b = 9
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