10010110110010

The binary sequence "10010110110010" is a string of ones and zeros commonly used in computing and digital systems to represent numerical values and data. In binary, each digit (or bit) corresponds to a power of two, with the rightmost bit representing 2^0 (1) and each subsequent bit to the left representing higher powers (2^1, 2^2, etc.). This sequence consists of 12 bits, making it a 12-bit binary number.

To convert "10010110110010" into its decimal (base-10) equivalent, each bit is multiplied by its corresponding power of two and summed. Breaking it down from right to left, the calculation is as follows:

(1×2^11) + (0×2^10) + (0×2^9) + (1×2^8) + (0×2^7) + (1×2^6) + (1×2^5) + (0×2^4) + (1×2^3) + (1×2^2) + (0×2^1) + (0×2^0), which equals 2048 + 0 + 0 + 256 + 0 + 64 + 32 + 0 + 8 + 4 + 0 + 0, totaling 2412 in decimal.

This binary sequence can also represent other data types depending on context, such as ASCII characters, hexadecimal values, or binary-coded decimal (BCD). For example, when interpreted as a hexadecimal value, "10010110110010" can be split into pairs of bits (from right to left): "0010 0101 1011 0010," which corresponds to the hexadecimal string "25B2." In ASCII, this hexadecimal value represents the characters "²" (superscript two) followed by "¢" (currency sign).

Such binary sequences are fundamental in digital electronics, programming, and data storage, serving as the basis for all computational operations. They are also used in error detection, cryptography, and encoding schemes to ensure data integrity and security.