ITPEC FE Morning October 2022 Question 32

255.255.255.224 — the prefix /27 means the first 27 bits of the mask are 1 and the remaining 5 are 0.

• •27 = 24 + 3: the first three octets are all ones, 255.255.255
• •The fourth octet has 3 one-bits: 11100000 = 128 + 64 + 32 = 224
• •The 5 host bits give 2⁵ = 32 addresses per subnet

Answer (b)

Why not others:

• •(a) 255.255.255.192 — 11000000 has only 2 one-bits in the last octet, so it is /26
• •(c) 255.255.255.248 — 11111000 has 5 one-bits, so it is /29
• •(d) 255.255.255.252 — 11111100 has 6 one-bits, so it is /30

Key rule: A last octet with n one-bits equals 256 − 2^{8 − n}: 128, 192, 224, 240, 248, 252, 254, 255 for n = 1 to 8.

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