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
A department needs 1471 host addresses in a single subnet. What is the longest prefix length p (smallest subnet) that is big enough?
1471 hosts
p =
2.IPv4 subnettingHard
A host has the address 172.20.40.228/20. What is the third octet x of its subnet's broadcast address?
172.20.40.228/20
x =
3.Computer networksMedium
Which protocol does the "ping" command use?
- AUDP
- BHTTP
- CICMP
- DTCP
4.Computer networksHard
By the Nyquist formula, what is the maximum bit rate of a noiseless 3 kHz channel using 4 signal levels?
- A6 kbit/s
- B24 kbit/s
- C3 kbit/s
- D12 kbit/s
5.Number systemsMedium
Write −72 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?
N = −728 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 0110 0011 >> 3. What is the result's value R in decimal?
0110 0011>> 3
R =
3Solutions
1.IPv4 subnetting
Answer: p = 21
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).
Host bits needed
210 − 2 = 1022 < 1471
211 − 2 = 2046 ≥ 1471 → h = 11
Prefix length
p = 32 − 11 = 21
Answer
p = /21
2.IPv4 subnetting
Answer: x = 47
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 in the third octet
24 = 16
Subnet of this host
network: 172.20.32.0
broadcast: 172.20.47.255
Answer
x = 47
3.Computer networks
Answer: C · ICMP
Why this is the answer
Ping sends ICMP echo requests and measures the time until echo replies return.
Answer
C · ICMP
4.Computer networks
Answer: D · 12 kbit/s
Why this is the answer
2 × 3000 × log₂ 4 = 2 × 3000 × 2 = 12,000 bit/s. More levels raise the rate, but noise limits how many can be told apart.
Answer
D · 12 kbit/s
5.Number systems
Answer: U = 184
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.
Invert and add one
72 = 0100 1000
inverted: 1011 0111
+1 → 1011 1000
Read it as unsigned
1011 1000₂ = 256 − 72 = 184
Answer
U = 184
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 right by 3 moves every bit 3 places to the right; bits that fall off the right end are lost and zeros come in on the left.
0110 0011 >> 3
= 0000 1100
Value of the result
0000 1100₂ = 12
Answer
R = 12
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