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 192.168.159.0/24 is divided into /26 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?
192.168.159.0/24/26subnet 2 (subnet 1 starts at .0)
x =
2.IPv4 subnettingHard
A host has the address 10.20.28.97/30. What is the last number (fourth octet) x of its subnet's broadcast address?
10.20.28.97/30
x =
3.Computer networksMedium
How many usable host addresses does a /26 IPv4 subnet have?
- A64
- B30
- C62
- D126
4.Computer networksHard
A path has 100 Mbit/s bandwidth and a 40 ms round-trip time. How much data must be in flight to keep it fully used?
- A500 kB
- B2.5 MB
- C4 kB
- D50 kB
5.Number systemsMedium
The 8-bit pattern 1101 1100 stores a signed integer in two's complement. What is its value N in decimal?
1101 11008 bit
N =
6.Number systemsHard
Set the bits to the 8-bit result of 1001 0001 XOR 0011 0101. What is the result's value R in decimal?
1001 0001XOR0011 0101
R =
3Solutions
1.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
26 = 64
Subnet number 2
network: (2 − 1)·64 = 64
broadcast: 64 + 64 − 1 = 127
Answer
x = 64
2.IPv4 subnetting
Answer: x = 99
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: ⌊97/4⌋·4 = 96
broadcast: 96 + 4 − 1 = 99
usable hosts: 97 … 98
Answer
x = 99
3.Computer networks
Answer: C · 62
Why this is the answer
A /26 has 6 host bits: 2⁶ = 64 addresses, minus the network and broadcast addresses, gives 62 usable hosts.
Answer
C · 62
4.Computer networks
Answer: A · 500 kB
Why this is the answer
The bandwidth-delay product is 100 × 10⁶ bit/s × 0.04 s = 4 × 10⁶ bits = 500 kB. The sender's window must be at least this large.
Answer
A · 500 kB
5.Number systems
Answer: N = −36
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.
Add the place values
The other bits keep their normal positive values.
−128 + 64 + 16 + 8 + 4 = −36
Answer
N = −36
6.Number systems
Answer: R = 164
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.
1001 0001
XOR 0011 0101
= 1010 0100
Value of the result
1010 0100₂ = 164
Answer
R = 164
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