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 255.255.255.224. How many usable host addresses H does it have?
255.255.255.224
H =
2.IPv4 subnettingHard
A router has routes to these networks: 10.153.137.0/24, 10.153.138.0/24, 10.153.139.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.153.137.0/24 … 10.153.139.0/24
p =
3.Computer networksMedium
Which subnet mask corresponds to /20?
- A255.255.248.0
- B255.255.224.0
- C255.255.240.0
- D255.255.255.240
4.Computer networksHard
Which of these addresses is a public (not RFC 1918 private) IPv4 address?
- A172.32.0.1
- B10.255.0.1
- C172.31.0.1
- D192.168.255.1
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 1101 1101 >> 2. What is the result's value R in decimal?
1101 1101>> 2
R =
3Solutions
1.IPv4 subnetting
Answer: H = 30
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
255.255.255.224 = /27
Usable hosts
25 − 2 = 30
Answer
H = 30
2.IPv4 subnetting
Answer: p = 22
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
137 = 10001001
139 = 10001011
common leading bits: 6
Prefix length
p = 16 + 6 = 22
Answer
p = /22
Summary route: 10.153.136.0/22 (it also covers 1 network(s) that are not in the list).
3.Computer networks
Answer: C · 255.255.240.0
Why this is the answer
/20 means 8 + 8 + 4 one-bits. Four one-bits in the third octet are 11110000 = 240, so the mask is 255.255.240.0.
Answer
C · 255.255.240.0
4.Computer networks
Answer: A · 172.32.0.1
Why this is the answer
172.16.0.0/12 runs from 172.16.0.0 to 172.31.255.255, so 172.32.0.1 lies outside it. The other three are in private ranges.
Answer
A · 172.32.0.1
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 = 55
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 2 moves every bit 2 places to the right; bits that fall off the right end are lost and zeros come in on the left.
1101 1101 >> 2
= 0011 0111
Value of the result
0011 0111₂ = 55
Answer
R = 55
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