Solution

The correct answer is Option 3) 101000001111

What is being asked?
Find the binary equivalent of the hexadecimal number (A0F)₁₆. (Here the middle character is the digit 0 “zero”, not the letter “O”.)

Method: Convert each hex digit to 4 binary bits

Concatenate the groups (left to right):
(A)(0)(F) → 1010 0000 1111 → 101000001111.

Quick check (back to hex): group in 4s from the left → 1010(A) 0000(0) 1111(F) ⇒ A0F ✔️

Why the other options are wrong

• Option 1) 111000111 – 9 bits (not a multiple of 4), so it cannot directly represent a whole number of hex digits; it does not map to A0F.
• Option 2) 101001111 – also 9 bits; grouping gives A 4 ? (not A0F).
• Option 4) 111100001010 – groups to 1111 0000 1010 = F0A (hex), which is A0F in reverse order.

Answer: 101000001111.