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 153 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
153 hosts
p =
2.IPv4 subnettingHard
The network 192.168.91.0/24 is split with VLSM for these LANs: A: 24 hosts, B: 4 hosts, C: 115 hosts, D: 18 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 A?
A: 24B: 4C: 115D: 18
x =
3.Computer networksMedium
Which TCP flag signals that a sender has finished sending data?
- AURG
- BSYN
- CFIN
- DPSH
4.Computer networksHard
What is the maximum transmission unit (MTU) of standard Ethernet payload?
- A1500 bytes
- B9000 bytes in every network
- C65,535 bytes
- D64 bytes
5.Number systemsMedium
Set the bits so they store −42 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −428 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 1110 1100 >> 3. What is the result's value R in decimal?
1110 1100>> 3
R =
3Solutions
1.IPv4 subnetting
Answer: p = 24
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
27 − 2 = 126 < 153
28 − 2 = 254 ≥ 153 → h = 8
Prefix length
p = 32 − 8 = 24
Answer
p = /24
2.IPv4 subnetting
Answer: x = 128
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: 115 hosts → 27 = 128 (/25)
A: 24 hosts → 25 = 32 (/27)
D: 18 hosts → 25 = 32 (/27)
B: 4 hosts → 23 = 8 (/29)
Allocation, largest first
C: .0 – .127
A: .128 – .159
D: .160 – .191
B: .192 – .199
Answer
x = 128
LAN A: 192.168.91.128/27.
3.Computer networks
Answer: C · FIN
Why this is the answer
Each side sends FIN when it has no more data, and the other side acknowledges it. SYN is for opening a connection; RST aborts one.
Answer
C · FIN
4.Computer networks
Answer: A · 1500 bytes
Why this is the answer
Standard Ethernet carries up to 1500 bytes of payload; larger IP packets must be fragmented or use path MTU discovery.
Answer
A · 1500 bytes
5.Number systems
Answer: U = 214
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
42 = 0010 1010
inverted: 1101 0101
+1 → 1101 0110
Read it as unsigned
1101 0110₂ = 256 − 42 = 214
Answer
U = 214
6.Number systems
Answer: R = 29
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 3 moves every bit 3 places to the right; bits that fall off the right end are lost and zeros come in on the left.
1110 1100 >> 3
= 0001 1101
Value of the result
0001 1101₂ = 29
Answer
R = 29
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