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
A host has the address 10.20.211.244/27. What is the last number (fourth octet) x of its subnet's broadcast address?
10.20.211.244/27
x =
3.Computer networksMedium
HTTP is stateless. How do websites usually keep a user logged in across requests?
- ABy storing the password in the URL
- BBy giving each user a fixed IP address
- CWith cookies holding a session identifier or token
- DBy keeping the TCP connection open for days
4.Computer networksHard
The count-to-infinity problem occurs in which kind of routing protocol, and what helps against it?
- ADistance-vector; split horizon and poison reverse
- BLink-state; flooding link updates
- CStatic routing; adding default routes
- DPath-vector; longer AS paths
5.Number systemsMedium
Set the bits so they store −34 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?
N = −348 bit
U =
6.Number systemsHard
Set the bits to the 8-bit result of 1000 1100 OR 1000 0101. What is the result's value R in decimal?
1000 1100OR1000 0101
R =
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 = 255
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
25 = 32
Subnet of this host
network: ⌊244/32⌋·32 = 224
broadcast: 224 + 32 − 1 = 255
usable hosts: 225 … 254
Answer
x = 255
3.Computer networks
Answer: C · With cookies holding a session identifier or token
Why this is the answer
The server sets a cookie containing a session ID or token, and the browser returns it with each request so the server can recognise the user.
Answer
C · With cookies holding a session identifier or token
4.Computer networks
Answer: A · 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
A · Distance-vector; split horizon and poison reverse
5.Number systems
Answer: U = 222
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
34 = 0010 0010
inverted: 1101 1101
+1 → 1101 1110
Read it as unsigned
1101 1110₂ = 256 − 34 = 222
Answer
U = 222
6.Number systems
Answer: R = 141
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
OR gives 1 where at least one bit is 1.
1000 1100
OR 1000 0101
= 1000 1101
Value of the result
1000 1101₂ = 141
Answer
R = 141
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