Question

two of the three following values are equal. which one is different from the others? 2e hexadecimal base 16 0010 1110 binary base 2 45 decimal base 10

Explanation:

Step1: Convert hexadecimal to decimal

The hexadecimal number \(2E_{16}\) is converted as follows: \(2\times16^{1}+14\times16^{0}=32 + 14=46\) (since \(E\) in hexadecimal represents 14 in decimal).

Step2: Convert binary to decimal

The binary number \(00101110_{2}\) is converted using the formula \(\sum_{i = 0}^{n - 1}a_{i}\times2^{i}\). Here, \(a_{0}=0,a_{1}=1,a_{2}=1,a_{3}=1,a_{4}=0,a_{5}=1,a_{6}=0,a_{7}=0\). So \(0\times2^{0}+1\times2^{1}+1\times2^{2}+1\times2^{3}+0\times2^{4}+1\times2^{5}+0\times2^{6}+0\times2^{7}=0 + 2+4 + 8+0 + 32+0+0 = 46\).

Step3: Analyze the decimal - given value

The given decimal value is \(45_{10}\).

Answer:

\(45\) (decimal)