102 eleven to denary number

To convert the base-11 number \(102_{11}\) to a denary (base-10) number, you can use the following formula: \[ \text{Value} = d_n \times b^n + d_{n-1} \times b^{n-1} + d_{n-2} \times b^{n-2} + \ldots + d_1 \times b^1 + d_0 \times b^0 \] where \(d\) represents the digits of the number, \(b\) is the base (in this case, 11), and \(n\) is the position of the digit from the right (starting at 0). For the number \(102_{11}\): - The digit \(1\) is in the \(11^2\) place (hundreds place in base-11). - The digit \(0\) is in the \(11^1\) place (tens place in base-11). - The digit \(2\) is in the \(11^0\) place (units place in base-11). Now, we can calculate the value: \[ 1 \times 11^2 + 0 \times 11^1 + 2 \times 11^0 \] Calculating each term: \[ 1 \times 121 + 0 \times 11 + 2 \times 1 = 121 + 0 + 2 = 123 \] Thus, the denary (base-10) equivalent of \(102_{11}\) is \(123_{10}\).