UPSC NDA II 2025 Mathematics Paper

Concept:Binary addition can be done by converting to decimal, adding, then converting the sum back to binary.Explanation:Convert $(10110110)_2$ to decimal:$10110110_2 = 1 \times 2^7 + 0 \times 2^6 + 1 \times 2^5 + 1 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 0 \times 2^0$$= 128 + 0 + 32 + 16 + 0 + 4 + 2 + 0 = 182$.Convert $(100011)_2$ to decimal:$100011_2 = 1 \times 2^5 + 0 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0$$= 32 + 0 + 0 + 0 + 2 + 1 = 35$.Add the decimal numbers: $182 + 35 = 217$.Convert $217$ back to binary by repeated division by 2:$217 \div 2 = 108$, remainder $1$$108 \div 2 = 54$, remainder $0$$54 \div 2 = 27$, remainder $0$$27 \div 2 = 13$, remainder $1$$13 \div 2 = 6$, remainder $1$$6 \div 2 = 3$, remainder $0$$3 \div 2 = 1$, remainder $1$$1 \div 2 = 0$, remainder $1$Reading remainders from bottom to top gives $110110001_2$.Answer:The sum is $(110110001)_2$, which matches option A.