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 192.168.131.0/24 is divided into /28 subnets, numbered 1, 2, 3, … from the lowest address (subnet 1 starts at .0). What is the fourth octet x of the network address of subnet 11?
192.168.131.0/24/28subnet 11 (subnet 1 starts at .0)
x =
2.IPv4 subnettingHard
A host has the address 10.20.176.64/30. What is the fourth octet x of its network address?
10.20.176.64/30
x =
3.Computer networksMedium
Which metric does RIP use to choose routes?
- AMeasured delay
- BHop count
- CBusiness policy
- DLink bandwidth
4.Computer networksHard
In the TCP/IP model, which layer adds port numbers?
- AInternet layer
- BApplication layer
- CTransport layer
- DLink layer
5.Number systemsMedium
Write −81 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?
N = −818 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0011 0110 XOR 1111 0001. What is the result's value R in decimal?
0011 0110XOR1111 0001
R =
3Solutions
1.IPv4 subnetting
Answer: x = 160
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
24 = 16
Subnet number 11
network: (11 − 1)·16 = 160
broadcast: 160 + 16 − 1 = 175
Answer
x = 160
2.IPv4 subnetting
Answer: x = 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).
Block size
22 = 4
Subnet of this host
network: ⌊64/4⌋·4 = 64
broadcast: 64 + 4 − 1 = 67
usable hosts: 65 … 66
Answer
x = 64
3.Computer networks
Answer: B · Hop count
Why this is the answer
RIP is a distance-vector protocol that counts hops, with 16 meaning unreachable. This limits it to small networks.
Answer
B · Hop count
4.Computer networks
Answer: C · Transport layer
Why this is the answer
TCP and UDP headers contain source and destination ports; the internet layer (IP) adds addresses.
Answer
C · Transport layer
5.Number systems
Answer: U = 175
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
81 = 0101 0001
inverted: 1010 1110
+1 → 1010 1111
Read it as unsigned
1010 1111₂ = 256 − 81 = 175
Answer
U = 175
6.Number systems
Answer: R = 199
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.
0011 0110
XOR 1111 0001
= 1100 0111
Value of the result
1100 0111₂ = 199
Answer
R = 199
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