NDA Mathematics Question (2025) — Solution

Step-by-step solution

Converting the given binary numbers to decimal: (101101101)_2 = 1 2^8 + 0 2^7 + 1 2^6 + 1 2^5 + 0 2^4 + 1 2^3 + 1 2^2 + 0 2^1 + 1 2^0 (101101101)_2 = 256 + 0 + 64 + 32 + 0 + 8 + 4 + 0 + 1 = 365 (100011)_2 = 1 2^5 + 0 2^4 + 0 2^3 + 0 2^2 + 1 2^1 + 1 2^0 (100011)_2 = 32 + 0 + 0 + 0 + 2 + 1 = 35 Adding the decimal values: Sum = 365 + 35 = 400 Converting 400 back to binary: 400 = 256 + 128 + 16 = 2^8 + 2^7 + 2^4 Therefore, 400 = (110010000)_2 Answer: (110010000)_2