10001011111

10001011111 is a binary number. In base 2, the digits represent powers of two. The rightmost digit represents 2^0, the next digit to the left represents 2^1, and so on. To convert 10001011111 to decimal, we sum the values of the positions where a '1' appears.

Starting from the right, the positions are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

The binary number 10001011111 has '1's in the positions corresponding to 2^0, 2^1, 2^2, 2^3, 2^5, and 2^10.

Calculating these powers of two:

2^0 = 1

2^1 = 2

2^2 = 4

2^3 = 8

2^5 = 32

2^10 = 1024

Summing these values: 1 + 2 + 4 + 8 + 32 + 1024 = 1071.

Therefore, the binary number 10001011111 is equivalent to the decimal number 1071. This conversion process is fundamental in computer science and digital electronics where binary representations are ubiquitous. Understanding how to convert between binary and decimal is crucial for interpreting data and understanding computational processes.