Decimal of hex 1A – UGC NET Question

To convert 1A₁₆ to decimal, we consider positional weights in base 16. The digit 1 is in the 16's place and represents 1×16. The digit A represents 10 in decimal and is in the 1's place, giving 10×1. Adding these yields 16 + 10 = 26. Thus, the decimal equivalent of 1A is 26.

Option A:
Option A suggests 20, which would come from a different combination of hex digits, such as 14₁₆. It does not equal 1×16 + 10, so it cannot be correct for 1A.

Option B:
Option B is correct because it follows the base-16 place value calculation: 1×16^1 + 10×16^0. This sum equals 26, which matches the required decimal value. It is a direct and accurate conversion.

Option C:
Option C gives 24, which would correspond to 18₁₆ if converted properly. The given hex number 1A does not produce this total. Therefore, 24 is not the correct equivalent.

Option D:
Option D suggests 30, which is larger than 26 and does not match the calculation 1×16 + 10. It would require different hex digits, such as 1E or 1E₁₆. Hence it cannot be right.