UPSC NDA I 2022 Mathematics Solved Paper

Concept:Convert binary numbers to decimal, perform the division in decimal, then convert the decimal quotient back to binary.Explanation:Binary numbers are converted to decimal by summing each digit multiplied by the appropriate power of $2$.For $(1110011)_2$, the expansion is $1 \times 2^6 + 1 \times 2^5 + 1 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0$, which equals $64 + 32 + 16 + 2 + 1 = 115$.For $(10111)_2$, the expansion is $1 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0$, which equals $16 + 4 + 2 + 1 = 23$.Now divide the decimal values: $115 \div 23 = 5$.Convert $5$ back to binary: $5 = 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = (101)_2$.Thus, $(1110011)_2 \div (10111)_2 = (101)_2$.Answer:$(101)_2$