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 192.168.10.0/24 must be divided into at least 3 equal subnets. If you borrow as few bits as possible, how many usable hosts H does each subnet have?
192.168.10.0/243 subnets
H =
2.IPv4 subnettingHard
A host has the address 10.20.104.157/29. What is the fourth octet x of its network address?
10.20.104.157/29
x =
3.Computer networksMedium
What is the purpose of the TCP three-way handshake?
- ATo close a connection quickly
- BTo encrypt the data
- CTo establish a connection and synchronise sequence numbers
- DTo find the IP address of a host before data can be sent to it
4.Computer networksHard
Why does a browser warn when a site presents a self-signed certificate?
- AThe certificate is always expired
- BNo trusted certificate authority vouches that the key belongs to that site
- CSelf-signed certificates use no encryption at all, so the traffic is sent in clear text
- DThe site must be using HTTP instead of HTTPS
5.Number systemsMedium
Set the bits so they store −17 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −178 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 1001 1010 OR 1001 0011. What is the result's value R in decimal?
1001 1010OR1001 0011
R =
3Solutions
1.IPv4 subnetting
Answer: H = 62
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).
Bits to borrow
22 = 4 ≥ 3 → b = 2, /26
Hosts per subnet
26 − 2 = 62
Answer
H = 62
2.IPv4 subnetting
Answer: x = 152
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 of this host
network: ⌊157/8⌋·8 = 152
broadcast: 152 + 8 − 1 = 159
usable hosts: 153 … 158
Answer
x = 152
3.Computer networks
Answer: C · To establish a connection and synchronise sequence numbers
Why this is the answer
The handshake sets up a connection and agrees initial sequence numbers on both sides before data is sent.
Answer
C · To establish a connection and synchronise sequence numbers
4.Computer networks
Answer: B · No trusted certificate authority vouches that the key belongs to that site
Why this is the answer
Browsers trust certificates signed, directly or through a chain, by CAs in their trust store. A self-signed certificate could be made by anyone, such as a man-in-the-middle.
Answer
B · No trusted certificate authority vouches that the key belongs to that site
5.Number systems
Answer: U = 239
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
17 = 0001 0001
inverted: 1110 1110
+1 → 1110 1111
Read it as unsigned
1110 1111₂ = 256 − 17 = 239
Answer
U = 239
6.Number systems
Answer: R = 155
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
OR gives 1 where at least one bit is 1.
1001 1010
OR 1001 0011
= 1001 1011
Value of the result
1001 1011₂ = 155
Answer
R = 155
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