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 10.6.56.0/22 is divided into equal subnets with prefix /28. How many subnets N are there?
10.6.56.0/22/28
N =
2.IPv4 subnettingHard
The network 192.168.209.0/24 is split with VLSM for these LANs: A: 22 hosts, B: 32 hosts, C: 119 hosts, D: 7 hosts. Subnets are allocated from .0 upwards, the LAN with the most hosts first, each with the smallest subnet that fits. What is the fourth octet x of the network address of LAN D?
A: 22B: 32C: 119D: 7
x =
3.Computer networksMedium
What does an MX record in DNS specify?
- AThe mail servers that accept email for a domain
- BThe IPv4 address of a web server
- CAn alias name for another host
- DThe name servers for a zone
4.Computer networksHard
What does TCP fast retransmit do?
- ASkips the three-way handshake when reconnecting to known hosts, so data is resent sooner
- BDoubles the window after every loss
- CResends every segment twice to be safe
- DResends a segment after three duplicate ACKs, without waiting for the timeout
5.Number systemsMedium
Set the bits so they store −45 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −458 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 1111 1001 AND 0100 0100. What is the result's value R in decimal?
1111 1001AND0100 0100
R =
3Solutions
1.IPv4 subnetting
Answer: N = 64
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).
Borrowed bits
28 − 22 = 6
Number of subnets
N = 26 = 64
Answer
N = 64
Each /28 subnet has 24 − 2 = 14 usable hosts.
2.IPv4 subnetting
Answer: x = 224
VLSM: each LAN gets the smallest subnet with 2ʰ − 2 ≥ its host count, i.e. prefix 32 − h. Allocating the largest subnets first keeps every block aligned on a multiple of its own size, so the network addresses follow by adding up the block sizes.
Block size per LAN
C: 119 hosts → 27 = 128 (/25)
B: 32 hosts → 26 = 64 (/26)
A: 22 hosts → 25 = 32 (/27)
D: 7 hosts → 24 = 16 (/28)
Allocation, largest first
C: .0 – .127
B: .128 – .191
A: .192 – .223
D: .224 – .239
Answer
x = 224
LAN D: 192.168.209.224/28.
3.Computer networks
Answer: A · The mail servers that accept email for a domain
Why this is the answer
MX (mail exchange) records list mail servers with priorities, so sending servers know where to deliver mail for that domain.
Answer
A · The mail servers that accept email for a domain
4.Computer networks
Answer: D · Resends a segment after three duplicate ACKs, without waiting for the timeout
Why this is the answer
Three duplicate ACKs strongly suggest a single lost segment, so TCP retransmits it at once. This recovers much faster than waiting for the retransmission timer.
Answer
D · Resends a segment after three duplicate ACKs, without waiting for the timeout
5.Number systems
Answer: U = 211
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
45 = 0010 1101
inverted: 1101 0010
+1 → 1101 0011
Read it as unsigned
1101 0011₂ = 256 − 45 = 211
Answer
U = 211
6.Number systems
Answer: R = 64
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
AND gives 1 only where both bits are 1.
1111 1001
AND 0100 0100
= 0100 0000
Value of the result
0100 0000₂ = 64
Answer
R = 64
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