100001111110000

100001111110000 is a binary number. In base-10, this number is equal to 17,488. Binary is a base-2 numeral system that uses only two symbols, typically "0" and "1". Each digit in a binary number is called a bit. The number 100001111110000 has fifteen bits. The rightmost bit represents 2^0, the next bit to the left represents 2^1, and so on. To convert this binary number to decimal, we can sum the products of each bit and its corresponding power of 2.

Starting from the rightmost bit, which is 0, we have 0 * 2^0 = 0. The next bit is 0, so 0 * 2^1 = 0. The next is 0, so 0 * 2^2 = 0. The next is 0, so 0 * 2^3 = 0. The next bit is 1, so 1 * 2^4 = 16. The next is 1, so 1 * 2^5 = 32. The next is 1, so 1 * 2^6 = 64. The next is 1, so 1 * 2^7 = 128. The next is 1, so 1 * 2^8 = 256. The next is 1, so 1 * 2^9 = 512. The next is 0, so 0 * 2^10 = 0. The next is 0, so 0 * 2^11 = 0. The next is 0, so 0 * 2^12 = 0. The next is 0, so 0 * 2^13 = 0. The leftmost bit is 1, so 1 * 2^14 = 16384.

Summing these values: 0 + 0 + 0 + 0 + 16 + 32 + 64 + 128 + 256 + 512 + 0 + 0 + 0 + 0 + 16384 = 17488. Therefore, the binary number 100001111110000 is equivalent to the decimal number 17,488. Binary numbers are fundamental in computer science and digital electronics, forming the basis of data representation and processing.