Question

question 16
the decimal equivalent of hexadecimal aa is ________.
165₁₀
176₁₀
186₁₀
170₁₀

Explanation:

Step1: Hexadecimal to decimal conversion formula

For a hexadecimal number \(AB_{16}\), the decimal equivalent is \(A\times16^{1}+B\times16^{0}\). Here \(A\) (first digit) and \(B\) (second digit) in hexadecimal \(AA_{16}\) both represent \(10\) (since \(A = 10\) in hexadecimal).

Step2: Substitute values into the formula

Substitute \(A = 10\) and \(B = 10\) into the formula: \(10\times16^{1}+10\times16^{0}\).

Step3: Calculate each term

\(10\times16^{1}=10\times16 = 160\) and \(10\times16^{0}=10\times1 = 10\).

Step4: Sum the terms

\(160 + 10=170\). So the decimal equivalent of hexadecimal \(AA\) is \(170_{10}\).

Answer:

170₁₀