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 10.139.104.0/22 is divided into equal subnets with prefix /28. How many subnets N are there?
10.139.104.0/22/28
N =
2.IPv4 subnettingHard
A host has the address 10.20.243.89/29. What is the fourth octet x of the last usable host address in its subnet?
10.20.243.89/29
x =
3.Computer networksMedium
What is a cyclic redundancy check (CRC) used for in Ethernet frames?
- ACorrecting every bit error automatically
- BChoosing the best route
- CEncrypting the frame
- DDetecting transmission errors
4.Computer networksHard
Which routing protocol is a link-state protocol?
- ARIP
- BARP
- COSPF
- DBGP
5.Number systemsMedium
Write −55 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?
N = −558 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0010 1111 XOR 0011 0110. What is the result's value R in decimal?
0010 1111XOR0011 0110
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 = 94
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
23 = 8
Subnet of this host
network: ⌊89/8⌋·8 = 88
broadcast: 88 + 8 − 1 = 95
usable hosts: 89 … 94
Answer
x = 94
3.Computer networks
Answer: D · Detecting transmission errors
Why this is the answer
The sender computes a CRC over the frame; the receiver recomputes it and discards the frame if they differ. CRC detects errors but does not correct them.
Answer
D · Detecting transmission errors
4.Computer networks
Answer: C · OSPF
Why this is the answer
OSPF routers build a full map of the area and compute shortest paths with Dijkstra's algorithm. RIP is distance-vector; BGP is path-vector.
Answer
C · OSPF
5.Number systems
Answer: U = 201
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.
Invert and add one
55 = 0011 0111
inverted: 1100 1000
+1 → 1100 1001
Read it as unsigned
1100 1001₂ = 256 − 55 = 201
Answer
U = 201
6.Number systems
Answer: R = 25
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.
0010 1111
XOR 0011 0110
= 0001 1001
Value of the result
0001 1001₂ = 25
Answer
R = 25
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