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 8 equal subnets. If you borrow as few bits as possible, how many usable hosts H does each subnet have?
192.168.10.0/248 subnets
H =
2.IPv4 subnettingHard
The network 192.168.180.0/24 is split with VLSM for these LANs: A: 22 hosts, B: 6 hosts, C: 16 hosts, D: 40 hosts, E: 14 hosts. Subnets are allocated from .0 upwards, the LAN with the most hosts first, each with the smallest subnet that fits. What is the fourth octet x of the network address of LAN C?
A: 22B: 6C: 16D: 40E: 14
x =
3.Computer networksMedium
A signal travels 2000 km through fibre at about 2 × 10⁸ m/s. What is the propagation delay?
- A0.1 ms
- B1 ms
- C10 ms
- D100 ms
4.Computer networksHard
Which routing protocol is a link-state protocol?
- AOSPF
- BBGP
- CRIP
- DARP
5.Number systemsMedium
Set the bits so they store −54 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −548 bit
U =
6.Number systemsHard
A system must give every one of 699 items its own binary code of the same length. What is the smallest number of bits b needed?
699
b = bit
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).
Bits to borrow
23 = 8 ≥ 8 → b = 3, /27
Hosts per subnet
25 − 2 = 30
Answer
H = 30
2.IPv4 subnetting
Answer: x = 96
VLSM: each LAN gets the smallest subnet with 2ʰ − 2 ≥ its host count, i.e. prefix 32 − h. Allocating the largest subnets first keeps every block aligned on a multiple of its own size, so the network addresses follow by adding up the block sizes.
Block size per LAN
D: 40 hosts → 26 = 64 (/26)
A: 22 hosts → 25 = 32 (/27)
C: 16 hosts → 25 = 32 (/27)
E: 14 hosts → 24 = 16 (/28)
B: 6 hosts → 23 = 8 (/29)
Allocation, largest first
D: .0 – .63
A: .64 – .95
C: .96 – .127
E: .128 – .143
B: .144 – .151
Answer
x = 96
LAN C: 192.168.180.96/27.
3.Computer networks
Answer: C · 10 ms
Why this is the answer
2 × 10⁶ m / 2 × 10⁸ m/s = 0.01 s = 10 ms. Propagation delay depends on distance and medium, not packet size.
Answer
C · 10 ms
4.Computer networks
Answer: A · OSPF
Why this is the answer
OSPF routers build a full map of the area and compute shortest paths with Dijkstra's algorithm. RIP is distance-vector; BGP is path-vector.
Answer
A · OSPF
5.Number systems
Answer: U = 202
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
54 = 0011 0110
inverted: 1100 1001
+1 → 1100 1010
Read it as unsigned
1100 1010₂ = 256 − 54 = 202
Answer
U = 202
6.Number systems
Answer: b = 10 bit
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.
Powers of two
29 = 512 < 699
210 = 1024 ≥ 699
Answer
b = 10
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