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 192.168.110.0/24 is divided into /27 subnets, numbered 1, 2, 3, … from the lowest address (subnet 1 starts at .0). What is the fourth octet x of the broadcast address of subnet 2?
192.168.110.0/24/27subnet 2 (subnet 1 starts at .0)
x =
2.IPv4 subnettingHard
A router has routes to these networks: 10.248.172.0/24, 10.248.173.0/24, 10.248.174.0/24, 10.248.175.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.248.172.0/24 … 10.248.175.0/24
p =
3.Computer networksMedium
Which protocol does the "ping" command use?
- AICMP
- BUDP
- CHTTP
- DTCP
4.Computer networksHard
TCP congestion control's "slow start" phase:
- AKeeps the window fixed at one segment
- BHalves the congestion window every round trip until a packet loss is detected
- CIs used only by UDP
- DIncreases the congestion window exponentially until a threshold or loss
5.Number systemsMedium
The 8-bit pattern 1110 1111 stores a signed integer in two's complement. What is its value N in decimal?
1110 11118 bit
N =
6.Number systemsHard
Set the bits to the 8-bit result of 0100 0010 XOR 0010 1110. What is the result's value R in decimal?
0100 0010XOR0010 1110
R =
3Solutions
1.IPv4 subnetting
Answer: x = 63
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
25 = 32
Subnet number 2
network: (2 − 1)·32 = 32
broadcast: 32 + 32 − 1 = 63
Answer
x = 63
2.IPv4 subnetting
Answer: p = 22
Route summarisation: a summary route a.b.c.0/p covers all networks whose first p bits match. Write the differing octet of the first and last network in binary; the number of common leading bits, plus the bits of the octets before it, is the longest summary prefix.
Compare the bits
172 = 10101100
175 = 10101111
common leading bits: 6
Prefix length
p = 16 + 6 = 22
Answer
p = /22
Summary route: 10.248.172.0/22
3.Computer networks
Answer: A · ICMP
Why this is the answer
Ping sends ICMP echo requests and measures the time until echo replies return.
Answer
A · ICMP
4.Computer networks
Answer: D · 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
D · Increases the congestion window exponentially until a threshold or loss
5.Number systems
Answer: N = −17
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.
Add the place values
The other bits keep their normal positive values.
−128 + 64 + 32 + 8 + 4 + 2 + 1 = −17
Answer
N = −17
6.Number systems
Answer: R = 108
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
XOR gives 1 where the two bits differ.
0100 0010
XOR 0010 1110
= 0110 1100
Value of the result
0110 1100₂ = 108
Answer
R = 108
ExamProblems · examproblems.com/courses/computer-networks