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 1052 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
1052 hosts
p =
2.IPv4 subnettingHard
A host has the address 10.20.250.136/28. What is the fourth octet x of its network address?
10.20.250.136/28
x =
3.Computer networksMedium
How does TLS typically use asymmetric and symmetric cryptography?
- AOnly asymmetric cryptography is used throughout
- BSymmetric methods agree keys and authenticate; asymmetric ciphers encrypt all the data
- CAsymmetric methods agree keys and authenticate; symmetric ciphers encrypt the data
- DOnly symmetric cryptography is used, with a fixed shared password
4.Computer networksHard
What is the main benefit of persistent connections (keep-alive) in HTTP/1.1?
- AThe server can push updates over UDP
- BSeveral requests reuse one TCP connection, avoiding repeated handshakes
- CThe connection stays encrypted without TLS
- DResponses can arrive in any order on one stream, so slow replies do not block others
5.Number systemsMedium
Set the bits so they store −70 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −708 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0110 0101 >> 2. What is the result's value R in decimal?
0110 0101>> 2
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 < 1052
211 − 2 = 2046 ≥ 1052 → h = 11
Prefix length
p = 32 − 11 = 21
Answer
p = /21
2.IPv4 subnetting
Answer: x = 128
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: ⌊136/16⌋·16 = 128
broadcast: 128 + 16 − 1 = 143
usable hosts: 129 … 142
Answer
x = 128
3.Computer networks
Answer: C · Asymmetric methods agree keys and authenticate; symmetric ciphers encrypt the data
Why this is the answer
Public-key methods and certificates set up a shared secret and prove identity. Fast symmetric ciphers such as AES then protect the bulk data.
Answer
C · Asymmetric methods agree keys and authenticate; symmetric ciphers encrypt the data
4.Computer networks
Answer: B · 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
B · Several requests reuse one TCP connection, avoiding repeated handshakes
5.Number systems
Answer: U = 186
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
70 = 0100 0110
inverted: 1011 1001
+1 → 1011 1010
Read it as unsigned
1011 1010₂ = 256 − 70 = 186
Answer
U = 186
6.Number systems
Answer: R = 25
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 2 moves every bit 2 places to the right; bits that fall off the right end are lost and zeros come in on the left.
0110 0101 >> 2
= 0001 1001
Value of the result
0001 1001₂ = 25
Answer
R = 25
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