100110000100010

100110000100010 is a binary number. In the decimal system, it represents the number 19458. Binary is a base-2 numeral system, meaning it uses only two symbols, typically 0 and 1. Each digit in a binary number is called a bit. This particular sequence of 15 bits, 100110000100010, can be converted to its decimal equivalent by summing the products of each bit and its corresponding power of 2, starting from the rightmost bit as 2^0.

The conversion process for 100110000100010 is as follows:

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

= 16384 + 0 + 0 + 2048 + 1024 + 0 + 0 + 0 + 0 + 32 + 0 + 0 + 0 + 2 + 0

= 19490.

This binary number, 100110000100010, has 15 digits. The number of bits in a binary representation can indicate the magnitude of the number it represents. For instance, a 15-bit number can represent values up to 2^15 - 1, which is 32767. Binary numbers are fundamental to computer science and digital electronics, as they form the basis of how data is stored and processed by computers.