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 192.168.10.0/24 must be divided into at least 30 equal subnets. If you borrow as few bits as possible, how many usable hosts H does each subnet have?
192.168.10.0/2430 subnets
H =
2.IPv4 subnettingHard
A router has routes to these networks: 10.36.113.0/24, 10.36.114.0/24, 10.36.115.0/24, 10.36.116.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.36.113.0/24 … 10.36.116.0/24
p =
3.Computer networksMedium
What is the role of a default gateway on a host?
- AIt is the switch port the host is connected to
- BIt is the DNS server
- CIt assigns MAC addresses
- DIt is the router used for traffic to other networks
4.Computer networksHard
Which mechanism prevents broadcast loops in a network with redundant switch links?
- ADHCP snooping
- BARP caching
- CSpanning Tree Protocol
- DNAT
5.Number systemsMedium
Set the bits so they store −72 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −728 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0011 0001 << 3. What is the result's value R in decimal?
0011 0001<< 3
R =
3Solutions
1.IPv4 subnetting
Answer: H = 6
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).
Bits to borrow
25 = 32 ≥ 30 → b = 5, /29
Hosts per subnet
23 − 2 = 6
Answer
H = 6
2.IPv4 subnetting
Answer: p = 21
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
113 = 01110001
116 = 01110100
common leading bits: 5
Prefix length
p = 16 + 5 = 21
Answer
p = /21
Summary route: 10.36.112.0/21 (it also covers 4 network(s) that are not in the list).
3.Computer networks
Answer: D · It is the router used for traffic to other networks
Why this is the answer
The host sends packets for non-local destinations to the default gateway, usually its local router.
Answer
D · It is the router used for traffic to other networks
4.Computer networks
Answer: C · 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
C · Spanning Tree Protocol
5.Number systems
Answer: U = 184
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
72 = 0100 1000
inverted: 1011 0111
+1 → 1011 1000
Read it as unsigned
1011 1000₂ = 256 − 72 = 184
Answer
U = 184
6.Number systems
Answer: R = 136
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 3 moves every bit 3 places to the left; bits that fall off the left end are lost and zeros come in on the right.
0011 0001 << 3
= 1000 1000
Value of the result
1000 1000₂ = 136
Answer
R = 136
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