Computer Networks · M2 · papers

Q2B · Department and lab allocation

Re-exam · 4 February 2026

Actual TEE paper · current-M2 matching parts; original marks

Actual PYQ. A university has been allocated an IP block of 172.16.0.0/16 (65,536 addresses) for its internal network. Department A: 32 labs, each requiring 128 addresses. Department B: 64 labs, each requiring 64 addresses. Department C: 16 labs, each requiring 512 addresses. Design the subnet allocations for each department and calculate how many IP addresses remain unused after the allocation. [10 marks]

Answer

Given

DepartmentLabsTotal addresses per lab
A32128
B6464
C16512

Parent: 172.16.0.0/16 with 65,536 addresses.

To find

Lab prefixes, department ranges and unused total addresses.

Formula and why

p=32-\log_2(N_{\mathrm{addresses\ per\ lab}})LaTeX: p=32-\log_2(N_{\mathrm{addresses\ per\ lab}})
N_{\mathrm{department}}=N_{\mathrm{labs}}N_{\mathrm{addresses\ per\ lab}}LaTeX: N_{\mathrm{department}}=N_{\mathrm{labs}}N_{\mathrm{addresses\ per\ lab}}

The question requests addresses, not usable hosts. Therefore do not add two before selecting each lab size.

Step-by-step solution

Step 1. Department A size

128=2⁷ addresses/lab → /25. 32×128=4,096 addresses → department block /20. Allocate 172.16.0.0/20, spanning 172.16.0.0–172.16.15.255.

Step 2. Department B size

64=2⁶ → /26 per lab. 64×64=4,096 → /20 department block. Allocate 172.16.16.0/20, spanning 172.16.16.0–172.16.31.255.

Step 3. Department C size

512=2⁹ → /23 per lab. 16×512=8,192 → /19 department block. Allocate 172.16.32.0/19, spanning 172.16.32.0–172.16.63.255. Its start at third octet 32 is aligned for /19.

Step 4. List every lab allocation

LabPrefixFirst addressLast address
A1172.16.0.0/25172.16.0.0172.16.0.127
A2172.16.0.128/25172.16.0.128172.16.0.255
A3172.16.1.0/25172.16.1.0172.16.1.127
A4172.16.1.128/25172.16.1.128172.16.1.255
A5172.16.2.0/25172.16.2.0172.16.2.127
A6172.16.2.128/25172.16.2.128172.16.2.255
A7172.16.3.0/25172.16.3.0172.16.3.127
A8172.16.3.128/25172.16.3.128172.16.3.255
A9172.16.4.0/25172.16.4.0172.16.4.127
A10172.16.4.128/25172.16.4.128172.16.4.255
A11172.16.5.0/25172.16.5.0172.16.5.127
A12172.16.5.128/25172.16.5.128172.16.5.255
A13172.16.6.0/25172.16.6.0172.16.6.127
A14172.16.6.128/25172.16.6.128172.16.6.255
A15172.16.7.0/25172.16.7.0172.16.7.127
A16172.16.7.128/25172.16.7.128172.16.7.255
A17172.16.8.0/25172.16.8.0172.16.8.127
A18172.16.8.128/25172.16.8.128172.16.8.255
A19172.16.9.0/25172.16.9.0172.16.9.127
A20172.16.9.128/25172.16.9.128172.16.9.255
A21172.16.10.0/25172.16.10.0172.16.10.127
A22172.16.10.128/25172.16.10.128172.16.10.255
A23172.16.11.0/25172.16.11.0172.16.11.127
A24172.16.11.128/25172.16.11.128172.16.11.255
A25172.16.12.0/25172.16.12.0172.16.12.127
A26172.16.12.128/25172.16.12.128172.16.12.255
A27172.16.13.0/25172.16.13.0172.16.13.127
A28172.16.13.128/25172.16.13.128172.16.13.255
A29172.16.14.0/25172.16.14.0172.16.14.127
A30172.16.14.128/25172.16.14.128172.16.14.255
A31172.16.15.0/25172.16.15.0172.16.15.127
A32172.16.15.128/25172.16.15.128172.16.15.255
B1172.16.16.0/26172.16.16.0172.16.16.63
B2172.16.16.64/26172.16.16.64172.16.16.127
B3172.16.16.128/26172.16.16.128172.16.16.191
B4172.16.16.192/26172.16.16.192172.16.16.255
B5172.16.17.0/26172.16.17.0172.16.17.63
B6172.16.17.64/26172.16.17.64172.16.17.127
B7172.16.17.128/26172.16.17.128172.16.17.191
B8172.16.17.192/26172.16.17.192172.16.17.255
B9172.16.18.0/26172.16.18.0172.16.18.63
B10172.16.18.64/26172.16.18.64172.16.18.127
B11172.16.18.128/26172.16.18.128172.16.18.191
B12172.16.18.192/26172.16.18.192172.16.18.255
B13172.16.19.0/26172.16.19.0172.16.19.63
B14172.16.19.64/26172.16.19.64172.16.19.127
B15172.16.19.128/26172.16.19.128172.16.19.191
B16172.16.19.192/26172.16.19.192172.16.19.255
B17172.16.20.0/26172.16.20.0172.16.20.63
B18172.16.20.64/26172.16.20.64172.16.20.127
B19172.16.20.128/26172.16.20.128172.16.20.191
B20172.16.20.192/26172.16.20.192172.16.20.255
B21172.16.21.0/26172.16.21.0172.16.21.63
B22172.16.21.64/26172.16.21.64172.16.21.127
B23172.16.21.128/26172.16.21.128172.16.21.191
B24172.16.21.192/26172.16.21.192172.16.21.255
B25172.16.22.0/26172.16.22.0172.16.22.63
B26172.16.22.64/26172.16.22.64172.16.22.127
B27172.16.22.128/26172.16.22.128172.16.22.191
B28172.16.22.192/26172.16.22.192172.16.22.255
B29172.16.23.0/26172.16.23.0172.16.23.63
B30172.16.23.64/26172.16.23.64172.16.23.127
B31172.16.23.128/26172.16.23.128172.16.23.191
B32172.16.23.192/26172.16.23.192172.16.23.255
B33172.16.24.0/26172.16.24.0172.16.24.63
B34172.16.24.64/26172.16.24.64172.16.24.127
B35172.16.24.128/26172.16.24.128172.16.24.191
B36172.16.24.192/26172.16.24.192172.16.24.255
B37172.16.25.0/26172.16.25.0172.16.25.63
B38172.16.25.64/26172.16.25.64172.16.25.127
B39172.16.25.128/26172.16.25.128172.16.25.191
B40172.16.25.192/26172.16.25.192172.16.25.255
B41172.16.26.0/26172.16.26.0172.16.26.63
B42172.16.26.64/26172.16.26.64172.16.26.127
B43172.16.26.128/26172.16.26.128172.16.26.191
B44172.16.26.192/26172.16.26.192172.16.26.255
B45172.16.27.0/26172.16.27.0172.16.27.63
B46172.16.27.64/26172.16.27.64172.16.27.127
B47172.16.27.128/26172.16.27.128172.16.27.191
B48172.16.27.192/26172.16.27.192172.16.27.255
B49172.16.28.0/26172.16.28.0172.16.28.63
B50172.16.28.64/26172.16.28.64172.16.28.127
B51172.16.28.128/26172.16.28.128172.16.28.191
B52172.16.28.192/26172.16.28.192172.16.28.255
B53172.16.29.0/26172.16.29.0172.16.29.63
B54172.16.29.64/26172.16.29.64172.16.29.127
B55172.16.29.128/26172.16.29.128172.16.29.191
B56172.16.29.192/26172.16.29.192172.16.29.255
B57172.16.30.0/26172.16.30.0172.16.30.63
B58172.16.30.64/26172.16.30.64172.16.30.127
B59172.16.30.128/26172.16.30.128172.16.30.191
B60172.16.30.192/26172.16.30.192172.16.30.255
B61172.16.31.0/26172.16.31.0172.16.31.63
B62172.16.31.64/26172.16.31.64172.16.31.127
B63172.16.31.128/26172.16.31.128172.16.31.191
B64172.16.31.192/26172.16.31.192172.16.31.255
C1172.16.32.0/23172.16.32.0172.16.33.255
C2172.16.34.0/23172.16.34.0172.16.35.255
C3172.16.36.0/23172.16.36.0172.16.37.255
C4172.16.38.0/23172.16.38.0172.16.39.255
C5172.16.40.0/23172.16.40.0172.16.41.255
C6172.16.42.0/23172.16.42.0172.16.43.255
C7172.16.44.0/23172.16.44.0172.16.45.255
C8172.16.46.0/23172.16.46.0172.16.47.255
C9172.16.48.0/23172.16.48.0172.16.49.255
C10172.16.50.0/23172.16.50.0172.16.51.255
C11172.16.52.0/23172.16.52.0172.16.53.255
C12172.16.54.0/23172.16.54.0172.16.55.255
C13172.16.56.0/23172.16.56.0172.16.57.255
C14172.16.58.0/23172.16.58.0172.16.59.255
C15172.16.60.0/23172.16.60.0172.16.61.255
C16172.16.62.0/23172.16.62.0172.16.63.255

Step 5. Calculate total allocation

4,096+4,096+8,192=16,384 addresses.

Step 6. Calculate unused space

65,536−16,384=49,152 addresses remain unallocated, from 172.16.64.0 through 172.16.255.255.

Final answer: A: /25 per lab; B: /26 per lab; C: /23 per lab. 49,152 total addresses remain unallocated.