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 255.255.255.128. How many usable host addresses H does it have?
255.255.255.128
H =
2.IPv4 subnettingHard
A host has the address 172.20.130.6/18. What is the third octet x of its network address?
172.20.130.6/18
x =
3.Computer networksMedium
Which metric does RIP use to choose routes?
- ABusiness policy
- BHop count
- CMeasured delay
- DLink bandwidth
4.Computer networksHard
Which mechanism prevents broadcast loops in a network with redundant switch links?
- ASpanning Tree Protocol
- BDHCP snooping
- CARP caching
- DNAT
5.Number systemsMedium
Set the bits so they store −85 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −858 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0110 1110 << 1. What is the result's value R in decimal?
0110 1110<< 1
R =
3Solutions
1.IPv4 subnetting
Answer: H = 126
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
255.255.255.128 = /25
Usable hosts
27 − 2 = 126
Answer
H = 126
2.IPv4 subnetting
Answer: x = 128
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
26 = 64
Subnet of this host
network: 172.20.128.0
broadcast: 172.20.191.255
Answer
x = 128
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: 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 = 171
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
85 = 0101 0101
inverted: 1010 1010
+1 → 1010 1011
Read it as unsigned
1010 1011₂ = 256 − 85 = 171
Answer
U = 171
6.Number systems
Answer: R = 220
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 left by 1 moves every bit 1 places to the left; bits that fall off the left end are lost and zeros come in on the right.
0110 1110 << 1
= 1101 1100
Value of the result
1101 1100₂ = 220
Answer
R = 220
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