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 172.20.0.0/16 is divided into equal subnets with prefix /23. How many subnets N are there?
172.20.0.0/16/23
N =
2.IPv4 subnettingHard
The network 192.168.207.0/24 is split with VLSM for these LANs: A: 8 hosts, B: 19 hosts, C: 60 hosts, D: 25 hosts, E: 6 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 A?
A: 8B: 19C: 60D: 25E: 6
x =
3.Computer networksMedium
A signal travels 2000 km through fibre at about 2 × 10⁸ m/s. What is the propagation delay?
- A1 ms
- B100 ms
- C10 ms
- D0.1 ms
4.Computer networksHard
In the TCP/IP model, which layer adds port numbers?
- ALink layer
- BApplication layer
- CInternet layer
- DTransport layer
5.Number systemsMedium
Set the bits so they store −74 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −748 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 1011 0011 >> 2. What is the result's value R in decimal?
1011 0011>> 2
R =
3Solutions
1.IPv4 subnetting
Answer: N = 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).
Borrowed bits
23 − 16 = 7
Number of subnets
N = 27 = 128
Answer
N = 128
Each /23 subnet has 29 − 2 = 510 usable hosts.
2.IPv4 subnetting
Answer: x = 128
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
C: 60 hosts → 26 = 64 (/26)
D: 25 hosts → 25 = 32 (/27)
B: 19 hosts → 25 = 32 (/27)
A: 8 hosts → 24 = 16 (/28)
E: 6 hosts → 23 = 8 (/29)
Allocation, largest first
C: .0 – .63
D: .64 – .95
B: .96 – .127
A: .128 – .143
E: .144 – .151
Answer
x = 128
LAN A: 192.168.207.128/28.
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: D · Transport layer
Why this is the answer
TCP and UDP headers contain source and destination ports; the internet layer (IP) adds addresses.
Answer
D · Transport layer
5.Number systems
Answer: U = 182
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
74 = 0100 1010
inverted: 1011 0101
+1 → 1011 0110
Read it as unsigned
1011 0110₂ = 256 − 74 = 182
Answer
U = 182
6.Number systems
Answer: R = 44
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.
1011 0011 >> 2
= 0010 1100
Value of the result
0010 1100₂ = 44
Answer
R = 44
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