The conversion of 11001 \(_2\) to base 10 equals_______

To convert a binary number to base 10, we start by writing down the binary digits of the number and assigning a place value to each digit, based on its position. The rightmost digit has a place value of 1, the next digit to the left has a place value of 2, then 4, 8, and so on, doubling each time. We then multiply each binary digit by its corresponding place value and add up the products. For the given binary number 11001, we can assign the following place values: 1 1 0 0 1 16 8 4 2 1 Multiplying each digit by its corresponding place value and adding up the products, we get: 1×16 + 1×8 + 0×4 + 0×2 + 1×1 = 16 + 8 + 1 = 25 Therefore, the conversion of 11001 \(_2\) to base 10 equals 25.