The decimal value of 4A9.2B is

[amp_mcq option1=”1193.1679″ option2=”119.31679″ option3=”11.931679″ option4=”1.1931679″ correct=”option1″]

This question was previously asked in

UPSC CISF-AC-EXE – 2024

The correct answer is A) 1193.1679. To convert a hexadecimal number (base 16) to a decimal number (base 10), we multiply each digit by 16 raised to the power of its position (starting from 0 for the digit before the decimal point, increasing to the left, and decreasing to the right). The hexadecimal digits are 0-9 and A-F (representing 10-15).
For 4A9.2B:
Integer part: 4A9 = 4 * 16^2 + A (10) * 16^1 + 9 * 16^0
= 4 * 256 + 10 * 16 + 9 * 1
= 1024 + 160 + 9 = 1193
Fractional part: .2B = 2 * 16^-1 + B (11) * 16^-2
= 2 / 16 + 11 / 256
= 1 / 8 + 11 / 256
= 32 / 256 + 11 / 256 = 43 / 256
Convert 43/256 to decimal: 43 ÷ 256 ≈ 0.16796875
Combining the integer and fractional parts: 1193 + 0.16796875 = 1193.16796875. This matches option A when rounded to four decimal places.

Hexadecimal to decimal conversion involves summing the products of each digit’s value and 16 raised to the power corresponding to its position relative to the decimal point.

The positions are assigned positive integers starting from 0 moving left from the decimal point (e.g., 16^0, 16^1, 16^2…) and negative integers moving right from the decimal point (e.g., 16^-1, 16^-2…).

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