110000010010010

The sequence 110000010010010 is a binary number. Binary is a base-2 numeral system that uses only two symbols, typically "0" and "1", to represent numbers. In the binary system, each digit's place value is a power of 2. The sequence 110000010010010, read from right to left, represents the sum of powers of 2 corresponding to the positions of the '1's.

To convert this binary number to its decimal equivalent, we assign place values starting from 2^0 on the far right. The sequence has 15 digits. The rightmost digit is 2^0, the next is 2^1, and so on, up to 2^14 for the leftmost digit.

The binary number 110000010010010 can be interpreted as:

1 * 2^14 + 1 * 2^13 + 0 * 2^12 + 0 * 2^11 + 0 * 2^10 + 0 * 2^9 + 0 * 2^8 + 1 * 2^7 + 0 * 2^6 + 0 * 2^5 + 1 * 2^4 + 0 * 2^3 + 0 * 2^2 + 1 * 2^1 + 0 * 2^0.

Calculating this sum:

16384 + 8192 + 0 + 0 + 0 + 0 + 0 + 128 + 0 + 0 + 16 + 0 + 0 + 2 + 0 = 24722.

Therefore, the binary sequence 110000010010010 is equivalent to the decimal number 24722. Binary numbers are fundamental in computing, forming the basis of how digital systems store and process information.