Which one of the following is the equivalent decimal value of Hexadeci

Which one of the following is the equivalent decimal value of Hexadecimal number 4A9.2 ?

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1192.125

1193.125

1192.0125

1193.0125

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This question was previously asked in

UPSC CISF-AC-EXE – 2021

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To convert a hexadecimal number to a decimal number, we multiply each digit by the corresponding power of the base (16) and sum the results. The weights for positions to the left of the decimal point are increasing positive powers of 16 (16^0, 16^1, 16^2, etc., from right to left). The weights for positions to the right of the decimal point are increasing negative powers of 16 (16^-1, 16^-2, etc., from left to right).
The hexadecimal number is 4A9.2. The digits are 4, A, 9, and 2. The hexadecimal digit ‘A’ corresponds to decimal 10.
Conversion:
4 * 16^2 + A * 16^1 + 9 * 16^0 + 2 * 16^-1
= 4 * 256 + 10 * 16 + 9 * 1 + 2 * (1/16)
= 1024 + 160 + 9 + 0.125
= 1193 + 0.125
= 1193.125

– Hexadecimal numbers are converted to decimal by summing the product of each digit and the corresponding power of 16.
– Hexadecimal digits A-F represent decimal values 10-15.

The decimal point in hexadecimal acts as the separator between positive and negative powers of the base, similar to the decimal point in the decimal system.

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