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 192.168.2.0/24 is divided into /25 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 2?
192.168.2.0/24/25subnet 2 (subnet 1 starts at .0)
x =
2.IPv4 subnettingHard
A router has routes to these networks: 10.230.107.0/24, 10.230.108.0/24, 10.230.109.0/24, 10.230.110.0/24, 10.230.111.0/24, 10.230.112.0/24, 10.230.113.0/24. What is the longest prefix length p of a single summary route that covers all of them?
10.230.107.0/24 … 10.230.113.0/24
p =
3.Computer networksMedium
Which TCP flag signals that a sender has finished sending data?
- AURG
- BSYN
- CPSH
- DFIN
4.Computer networksHard
In a TCP connection, what does the receive window (rwnd) control?
- AThe size of each IP packet header
- BThe number of open ports
- CHow much unacknowledged data the sender may send, based on the receiver's buffer
- DThe retransmission time-out, calculated from the measured round-trip time of each segment
5.Number systemsMedium
Set the bits so they store −66 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −668 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 1000 0110 << 1. What is the result's value R in decimal?
1000 0110<< 1
R =
3Solutions
1.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
27 = 128
Subnet number 2
network: (2 − 1)·128 = 128
broadcast: 128 + 128 − 1 = 255
Answer
x = 128
2.IPv4 subnetting
Answer: p = 19
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
107 = 01101011
113 = 01110001
common leading bits: 3
Prefix length
p = 16 + 3 = 19
Answer
p = /19
Summary route: 10.230.96.0/19 (it also covers 25 network(s) that are not in the list).
3.Computer networks
Answer: D · FIN
Why this is the answer
Each side sends FIN when it has no more data, and the other side acknowledges it. SYN is for opening a connection; RST aborts one.
Answer
D · FIN
4.Computer networks
Answer: C · How much unacknowledged data the sender may send, based on the receiver's buffer
Why this is the answer
The receiver advertises how much buffer space it has; the sender limits unacknowledged data accordingly, preventing receiver overload.
Answer
C · How much unacknowledged data the sender may send, based on the receiver's buffer
5.Number systems
Answer: U = 190
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
66 = 0100 0010
inverted: 1011 1101
+1 → 1011 1110
Read it as unsigned
1011 1110₂ = 256 − 66 = 190
Answer
U = 190
6.Number systems
Answer: R = 12
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.
1000 0110 << 1
= 0000 1100
Value of the result
0000 1100₂ = 12
Answer
R = 12
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