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 10.167.247.0/24 is divided into equal subnets with prefix /26. How many subnets N are there?
10.167.247.0/24/26
N =
2.IPv4 subnettingHard
A host has the address 10.20.221.230/26. What is the fourth octet x of the last usable host address in its subnet?
10.20.221.230/26
x =
3.Computer networksMedium
NAT (network address translation) is mainly used to:
- ATranslate domain names into IP addresses for devices on a local network
- BEncrypt traffic between two sites
- CLet many devices with private addresses share one public IP address
- DIncrease the speed of a network cable
4.Computer networksHard
The count-to-infinity problem occurs in which kind of routing protocol, and what helps against it?
- APath-vector; longer AS paths
- BLink-state; flooding link updates
- CDistance-vector; split horizon and poison reverse
- DStatic routing; adding default routes
5.Number systemsMedium
Set the bits so they store −23 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −238 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 1011 0000 XOR 0110 1000. What is the result's value R in decimal?
1011 0000XOR0110 1000
R =
3Solutions
1.IPv4 subnetting
Answer: N = 4
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).
Borrowed bits
26 − 24 = 2
Number of subnets
N = 22 = 4
Answer
N = 4
Each /26 subnet has 26 − 2 = 62 usable hosts.
2.IPv4 subnetting
Answer: x = 254
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 of this host
network: ⌊230/64⌋·64 = 192
broadcast: 192 + 64 − 1 = 255
usable hosts: 193 … 254
Answer
x = 254
3.Computer networks
Answer: C · Let many devices with private addresses share one public IP address
Why this is the answer
NAT rewrites addresses (and ports) so private networks can access the internet through a smaller number of public addresses.
Answer
C · Let many devices with private addresses share one public IP address
4.Computer networks
Answer: C · Distance-vector; split horizon and poison reverse
Why this is the answer
After a failure, distance-vector routers can keep advertising stale routes to each other, raising the metric slowly. Split horizon, poison reverse and a maximum metric limit this.
Answer
C · Distance-vector; split horizon and poison reverse
5.Number systems
Answer: U = 233
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
23 = 0001 0111
inverted: 1110 1000
+1 → 1110 1001
Read it as unsigned
1110 1001₂ = 256 − 23 = 233
Answer
U = 233
6.Number systems
Answer: R = 216
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.
1011 0000
XOR 0110 1000
= 1101 1000
Value of the result
1101 1000₂ = 216
Answer
R = 216
ExamProblems · examproblems.com/courses/computer-networks