SSC IMD SA 2017 – Question 166

A network requires 29 subnets while maximizing the number of available host addresses per subnet. How many bits must be borrowed from the host field to provide the correct subnet mask?

• 3
• 4
• 6
• 5

Detailed Explanation:

The correct answer is d) 5.

Problem Formulation:

We are required to create at least 29 subnets while maximizing the number of host addresses available on each subnet. We need to determine how many bits ($s$) must be borrowed from the host field.

Mathematical Calculation:

• The number of subnets that can be created by borrowing $s$ bits from the host field is given by the formula:$$\text{Number of Subnets} = 2^s$$
• We require:$$2^s \ge 29$$
• Testing integer values for $s$:
  • If $s = 3 \implies 2^3 = 8 < 29$ (Insufficient)
  • If $s = 4 \implies 2^4 = 16 < 29$ (Insufficient)
  • If $s = 5 \implies 2^5 = 32 \ge 29$ (Sufficient)
  • If $s = 6 \implies 2^6 = 64 \ge 29$ (Sufficient, but leaves fewer host bits)
• To maximize the available host addresses per subnet, we must preserve as many host bits ($h$) as possible, which requires borrowing the minimum number of bits that satisfies the subnet requirement ($2^h – 2$).
• The minimum value of $s$ that satisfies $2^s \ge 29$ is $s = 5$.