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 subnet uses the mask 255.255.240.0. How many usable host addresses H does it have?
255.255.240.0
H =
2.IPv4 subnettingHard
The network 192.168.219.0/24 is split with VLSM for these LANs: A: 27 hosts, B: 8 hosts, C: 50 hosts, D: 49 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: 27B: 8C: 50D: 49
x =
3.Computer networksMedium
Which subnet mask corresponds to /20?
- A255.255.255.240
- B255.255.224.0
- C255.255.248.0
- D255.255.240.0
4.Computer networksHard
TCP congestion control's "slow start" phase:
- AHalves the congestion window every round trip until a packet loss is detected
- BIs used only by UDP
- CIncreases the congestion window exponentially until a threshold or loss
- DKeeps the window fixed at one segment
5.Number systemsMedium
Set the bits so they store −37 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −378 bit
U =
6.Number systemsHard
What is the most negative integer N that can be stored in 32-bit two's complement?
32 bit
N =
3Solutions
1.IPv4 subnetting
Answer: H = 4094
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).
Prefix length
255.255.240.0 = /20
Usable hosts
212 − 2 = 4094
Answer
H = 4094
2.IPv4 subnetting
Answer: x = 64
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: 50 hosts → 26 = 64 (/26)
D: 49 hosts → 26 = 64 (/26)
A: 27 hosts → 25 = 32 (/27)
B: 8 hosts → 24 = 16 (/28)
Allocation, largest first
C: .0 – .63
D: .64 – .127
A: .128 – .159
B: .160 – .175
Answer
x = 64
LAN D: 192.168.219.64/26.
3.Computer networks
Answer: D · 255.255.240.0
Why this is the answer
/20 means 8 + 8 + 4 one-bits. Four one-bits in the third octet are 11110000 = 240, so the mask is 255.255.240.0.
Answer
D · 255.255.240.0
4.Computer networks
Answer: C · Increases the congestion window exponentially until a threshold or loss
Why this is the answer
Slow start grows the congestion window exponentially; after the threshold, congestion avoidance grows it linearly, and loss reduces it.
Answer
C · Increases the congestion window exponentially until a threshold or loss
5.Number systems
Answer: U = 219
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
37 = 0010 0101
inverted: 1101 1010
+1 → 1101 1011
Read it as unsigned
1101 1011₂ = 256 − 37 = 219
Answer
U = 219
6.Number systems
Answer: N = −2.147 × 10⁹
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.
Most negative value
−231 = −2147483648
Answer
N = −2147483648
ExamProblems · examproblems.com/courses/computer-networks