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 192.168.56.0/24 is divided into /28 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 12?
192.168.56.0/24/28subnet 12 (subnet 1 starts at .0)
x =
2.IPv4 subnettingHard
A host has the address 10.20.61.195/28. What is the fourth octet x of its network address?
10.20.61.195/28
x =
3.Computer networksMedium
NAT (network address translation) is mainly used to:
- ATranslate domain names into IP addresses for devices on a local network
- BIncrease the speed of a network cable
- CLet many devices with private addresses share one public IP address
- DEncrypt traffic between two sites
4.Computer networksHard
What is the main benefit of persistent connections (keep-alive) in HTTP/1.1?
- ASeveral requests reuse one TCP connection, avoiding repeated handshakes
- BThe server can push updates over UDP
- CResponses can arrive in any order on one stream, so slow replies do not block others
- DThe connection stays encrypted without TLS
5.Number systemsMedium
The 8-bit pattern 1111 0000 stores a signed integer in two's complement. What is its value N in decimal?
1111 00008 bit
N =
6.Number systemsHard
Set the bits to the 8-bit result of 0111 1001 << 1. What is the result's value R in decimal?
0111 1001<< 1
R =
3Solutions
1.IPv4 subnetting
Answer: x = 176
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
24 = 16
Subnet number 12
network: (12 − 1)·16 = 176
broadcast: 176 + 16 − 1 = 191
Answer
x = 176
2.IPv4 subnetting
Answer: x = 192
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
24 = 16
Subnet of this host
network: ⌊195/16⌋·16 = 192
broadcast: 192 + 16 − 1 = 207
usable hosts: 193 … 206
Answer
x = 192
3.Computer networks
Answer: C · Let many devices with private addresses share one public IP address
Why this is the answer
NAT rewrites addresses (and ports) so private networks can access the internet through a smaller number of public addresses.
Answer
C · Let many devices with private addresses share one public IP address
4.Computer networks
Answer: A · Several requests reuse one TCP connection, avoiding repeated handshakes
Why this is the answer
Reusing a connection avoids a new handshake and slow start for each object, so pages with many resources load faster.
Answer
A · Several requests reuse one TCP connection, avoiding repeated handshakes
5.Number systems
Answer: N = −16
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 + 32 + 16 = −16
Answer
N = −16
6.Number systems
Answer: R = 242
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 1 moves every bit 1 places to the left; bits that fall off the left end are lost and zeros come in on the right.
0111 1001 << 1
= 1111 0010
Value of the result
1111 0010₂ = 242
Answer
R = 242
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