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 1579 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
1579 hosts
p =
2.IPv4 subnettingHard
A host has the address 172.20.52.225/21. What is the third octet x of its subnet's broadcast address?
172.20.52.225/21
x =
3.Computer networksMedium
Which range of TCP/UDP port numbers is reserved as "well-known" ports?
- A1024–49151
- B49152–65535
- C0–65535
- D0–1023
4.Computer networksHard
Which mechanism prevents broadcast loops in a network with redundant switch links?
- ASpanning Tree Protocol
- BARP caching
- CNAT
- DDHCP snooping
5.Number systemsMedium
Set the bits so they store −10 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −108 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 1000 1111 >> 1. What is the result's value R in decimal?
1000 1111>> 1
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 < 1579
211 − 2 = 2046 ≥ 1579 → h = 11
Prefix length
p = 32 − 11 = 21
Answer
p = /21
2.IPv4 subnetting
Answer: x = 55
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 in the third octet
23 = 8
Subnet of this host
network: 172.20.48.0
broadcast: 172.20.55.255
Answer
x = 55
3.Computer networks
Answer: D · 0–1023
Why this is the answer
Ports 0–1023 are well-known ports for standard services. 1024–49151 are registered ports and 49152–65535 are dynamic or private ports.
Answer
D · 0–1023
4.Computer networks
Answer: A · Spanning Tree Protocol
Why this is the answer
STP elects a root bridge and blocks redundant paths, unblocking them if an active link fails.
Answer
A · Spanning Tree Protocol
5.Number systems
Answer: U = 246
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
10 = 0000 1010
inverted: 1111 0101
+1 → 1111 0110
Read it as unsigned
1111 0110₂ = 256 − 10 = 246
Answer
U = 246
6.Number systems
Answer: R = 71
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 1 moves every bit 1 places to the right; bits that fall off the right end are lost and zeros come in on the left.
1000 1111 >> 1
= 0100 0111
Value of the result
0100 0111₂ = 71
Answer
R = 71
ExamProblems · examproblems.com/courses/computer-networks