Convert $(AD)_{16}$ to Decimal

The task is to find number system equivalents for $(AD)_{16}$. First, convert $(AD)_{16}$ to base-10 (decimal).

In base-16 (hexadecimal), A = 10 and D = 13. The conversion is: $(AD)_{16} = (10 \times 16^1) + (13 \times 16^0) = (10 \times 16) + (13 \times 1) = 160 + 13 = (173)_{10}$.

Thus, $(AD)_{16}$ is equivalent to $(173)_{10}$.

Evaluate Options for Equivalence to $(173)_{10}$

Option A: $(255)_8$

Convert octal $(255)_8$ to decimal:

$(255)_8 = (2 \times 8^2) + (5 \times 8^1) + (5 \times 8^0) = (2 \times 64) + (5 \times 8) + (5 \times 1) = 128 + 40 + 5 = (173)_{10}$. Equivalent.

Option B: $(10101101)_2$

Convert binary $(10101101)_2$ to decimal:

$(10101101)_2 = (1 \times 2^7) + (0 \times 2^6) + (1 \times 2^5) + (0 \times 2^4) + (1 \times 2^3) + (1 \times 2^2) + (0 \times 2^1) + (1 \times 2^0)$
$= 128 + 0 + 32 + 0 + 8 + 4 + 0 + 1 = (173)_{10}$. Equivalent.

Option C: $(173)_{10}$

This number is already in decimal form $(173)_{10}$. Equivalent.

Option D: $(1141)_5$

Convert base-5 $(1141)_5$ to decimal:

$(1141)_5 = (1 \times 5^3) + (1 \times 5^2) + (4 \times 5^1) + (1 \times 5^0) = (1 \times 125) + (1 \times 25) + (4 \times 5) + (1 \times 1) = 125 + 25 + 20 + 1 = (171)_{10}$. This is not equal to $(173)_{10}$. Not Equivalent.

Final Answer Selection

The numbers equivalent to $(AD)_{16}$ are the options A, B, and C.

The correct choice is the one that states "A, B and C only".